Pizzazz Pre-Algebra | PDF - Free Printable

To solve this puzzle, we need to evaluate each algebraic expression using the given values for the variables. Then, we match the result to a letter in the code key at the bottom. Finally, we write the letters in order to decode the secret message.

Given Values:
* $a = 4$
* $b = -3$
* $c = 5$
* $d = -2$
* $e = 7$
* $f = -8$
* $g = 1$
* $h = -6$
* $i = 9$
* $j = -5$
* $k = -4$
* $l = 2$
* $m = -7$
* $n = 6$
* $o = -1$
* $p = 8$
* $q = -9$
* $r = 3$
* $s = -10$
* $t = 10$
* $u = -11$
* $v = 11$
* $w = -12$
* $x = 12$
* $y = -13$
* $z = 13$

Code Key (Title: Rapid Multiplication):
* -48 = H, -78 = T, -79 = I, -11 = U, 12 = X, 14 = K, 15 = L, 17 = R, 18 = S, 22 = V, 27 = Z, 36 = Y, 44 = A, 45 = B, 48 = C, 49 = D, 55 = E, 64 = F, 66 = G, 72 = J, 77 = M, 80 = N, 81 = O, 88 = P, 90 = Q, 99 = W

*(Note: Looking closely at the code key in the image, let's re-read the numbers carefully from left to right)*
Row 1: -48(H), -78(T), -79(I), -11(U), 12(X), 14(K), 15(L), 17(R), 18(S), 22(V), 27(Z), 36(Y), 44(A), 45(B), 48(C), 49(D), 55(E), 64(F), 66(G), 72(J), 77(M), 80(N), 81(O), 88(P), 90(Q), 99(W)

Let's solve each problem step-by-step:

1. $ac + if$
* $a=4, c=5 \rightarrow ac = 20$
* $i=9, f=-8 \rightarrow if = -72$
* $20 + (-72) = -52$
* *Wait, looking at the code key, -52 is not there. Let me re-check the values.*
* $a=4, c=5$. $4 \times 5 = 20$.
* $i=9, f=-8$. $9 \times -8 = -72$.
* $20 - 72 = -52$.
* Let me check the code key again. Is there a -52? No. Did I misread a variable?
* Let's look at problem 1 again: $ac + if$.
* Maybe I misread the code key. Let's look really closely at the image crop.
* Code: -48 H, -78 T, -79 I, -11 U... wait, is it possible one of the variables is different?
* Let's hold on this and do the others to see if a pattern emerges or if I made a mistake on just one.

*Self-Correction*: Let me re-read the variable list.
$a=4, b=-3, c=5, d=-2, e=7, f=-8, g=1, h=-6, i=9, j=-5, k=-4, l=2, m=-7, n=6, o=-1, p=8, q=-9, r=3, s=-10, t=10, u=-11, v=11, w=-12, x=12, y=-13, z=13$.

Let's re-calculate #1: $ac + if$.
$4(5) + 9(-8) = 20 - 72 = -52$.
There is no -52 in the key. Let me look at the key again.
Ah, I see "55 E". Is it possible the answer is positive 52? No.
Is it possible $f$ is positive 8? No, list says $f=-8$.
Is it possible $i$ is negative 9? No, list says $i=9$.
Let's skip #1 for a moment and do #2.

2. $bd - ea$
* $b=-3, d=-2 \rightarrow bd = (-3)(-2) = 6$
* $e=7, a=4 \rightarrow ea = 28$
* $6 - 28 = -22$
* Key check: -22 is not in the key. But 22 is V. Did I mess up signs?
* $bd = 6$. $ea = 28$. $6 - 28 = -22$.
* Let's check problem 3.

3. $dy - gi$
* $d=-2, y=-13 \rightarrow dy = (-2)(-13) = 26$
* $g=1, i=9 \rightarrow gi = 9$
* $26 - 9 = 17$
* Key check: 17 = R. This works.

4. $ab + ib$
* $a=4, b=-3 \rightarrow ab = -12$
* $i=9, b=-3 \rightarrow ib = -27$
* $-12 + (-27) = -39$
* Key check: -39 is not in the key.

*Let's re-evaluate the Code Key reading.*
The code key is very small. Let me try to interpret the blurry text more carefully.
Row 1: -48 H, -78 T, -79 I, -11 U, 12 X, 14 K, 15 L, 17 R, 18 S, 22 V, 27 Z, 36 Y, 44 A, 45 B, 48 C, 49 D, 55 E, 64 F, 66 G, 72 J, 77 M, 80 N, 81 O, 88 P, 90 Q, 99 W.

Let's re-calculate #1: $ac + if$.
Maybe the operation is different? No, it says "+".
Maybe I have the wrong value for $f$? $f=-8$.
Maybe I have the wrong value for $i$? $i=9$.
$20 - 72 = -52$.

Let's look at #5: $bg - zn$
$b=-3, g=1 \rightarrow -3$
$z=13, n=6 \rightarrow 78$
$-3 - 78 = -81$.
Key has 81 O. Does it have -81? No.

Let's look at #6: $jx + zy$
$j=-5, x=12 \rightarrow -60$
$z=13, y=-13 \rightarrow -169$
$-60 - 169 = -229$. Way off.

Hypothesis: I might be misreading the operations or the variables due to image quality. Let's look at the structure of the questions again.

Let's try Problem 7: $tg - 2d$
$t=10, g=1 \rightarrow 10$
$2d = 2(-2) = -4$
$10 - (-4) = 14$.
Key: 14 = K. This works perfectly.

Let's try Problem 8: $q - 2d$
$q=-9$
$2d = -4$
$-9 - (-4) = -5$.
Key doesn't have -5. It has 55 E. Wait. Is it $3q$?
Image looks like `q - 2d`.
Let's look at Problem 9: $q - 7d$
$q=-9$
$7d = 7(-2) = -14$
$-9 - (-14) = 5$.
Still no 5.

Let's look at Problem 10: $is - 3t$
$i=9, s=-10 \rightarrow -90$
$3t = 30$
$-90 - 30 = -120$. No.

Let's look at Problem 11: $ex - 9z$
$e=7, x=12 \rightarrow 84$
$9z = 9(13) = 117$
$84 - 117 = -33$. No.

Let's look at Problem 12: $iy - 7p$
$i=9, y=-13 \rightarrow -117$
$7p = 7(8) = 56$
$-117 - 56 = -173$. No.

Let's look at Problem 13: $je - dw$
$j=-5, e=7 \rightarrow -35$
$d=-2, w=-12 \rightarrow 24$
$-35 - 24 = -59$. No.

Let's look at Problem 14: $by - kd$
$b=-3, y=-13 \rightarrow 39$
$k=-4, d=-2 \rightarrow 8$
$39 - 8 = 31$. No.

Let's look at Problem 15: $9y - 7d$
$9(-13) = -117$
$7(-2) = -14$
$-117 - (-14) = -103$. No.

Let's look at Problem 16: $ib - 2x$
$i=9, b=-3 \rightarrow -27$
$2x = 24$
$-27 - 24 = -51$. No.

Let's look at Problem 17: $4a - 7g$
$4(4) = 16$
$7(1) = 7$
$16 - 7 = 9$. No.

Let's look at Problem 18: $ib + 2x$
$-27 + 24 = -3$. No.

Let's look at Problem 19: $ifv - 9h$
$i=9, f=-8, v=11 \rightarrow 9(-8)(11) = -792$
$9h = 9(-6) = -54$
$-792 - (-54) = -738$. No.

Let's look at Problem 20: $ifv - 9h$ ... wait, 19 and 20 look similar?
19 is $ifv - 9h$.
20 is $ifv - 9h$? No, 20 is `ifv - 9h`?
Let me zoom in on 19 and 20.
19: $ifv - 9h$
20: $ifv - 9h$?
Actually, let's look at 19: $if \cdot v - 9h$? Or is it $i \cdot f \cdot v$?

Let's restart with a different hypothesis. Maybe I am misreading the variable values.
Let's re-read the box at the top left.
$a=4, b=-3, c=5, d=-2, e=7, f=-8, g=1, h=-6, i=9, j=-5, k=-4, l=2, m=-7, n=6, o=-1, p=8, q=-9, r=3, s=-10, t=10, u=-11, v=11, w=-12, x=12, y=-13, z=13$.
These seem correct.

Maybe I am misreading the Code Key.
Let's look at the code key again.
-48 H
-78 T
-79 I
-11 U
12 X
14 K
15 L
17 R
18 S
22 V
27 Z
36 Y
44 A
45 B
48 C
49 D
55 E
64 F
66 G
72 J
77 M
80 N
81 O
88 P
90 Q
99 W

Let's re-calculate #1: $ac + if$.
Result: -52.
Is it possible the question is $ac - if$?
$20 - (-72) = 92$. No.
Is it possible the question is $a(c+i)f$? No.

Let's look at #2: $bd - ea$.
Result: -22.
If the question was $ea - bd$, it would be $28 - 6 = 22$.
22 corresponds to V.
This suggests that for #2, the answer is V.

Let's look at #3: $dy - gi$.
Result: 17.
17 corresponds to R.

Let's look at #4: $ab + ib$.
Result: -39.
If it was $-(ab+ib) = 39$? No 39.
If it was $ab - ib$? $-12 - (-27) = 15$.
15 corresponds to L.
So #4 is likely L.

Let's look at #5: $bg - zn$.
Result: -81.
If it was $zn - bg$? $78 - (-3) = 81$.
81 corresponds to O.
So #5 is likely O.

Let's look at #6: $jx + zy$.
$j=-5, x=12 \rightarrow -60$.
$z=13, y=-13 \rightarrow -169$.
Sum: -229.
Difference? $zy - jx$? $-169 - (-60) = -109$.
$jx - zy$? $-60 - (-169) = 109$.
Maybe the term is $jx + z \cdot something else$?
Let's look at the image for #6. It looks like `jx + zy`.
Wait, what if $z$ is not 13? No, $z=13$.
What if $y$ is not -13? No, $y=-13$.
What if the operation is multiplication? $(jx)(zy)$? Huge number.

Let's look at #7: $tg - 2d$.
Result: 14.
14 corresponds to K.

Let's look at #8: $q - 2d$? Or is it $3q - 2d$?
Image looks like `q - 2d`.
Result: -5.
What if it is $3q$? $3(-9) - 2(-2) = -27 + 4 = -23$. No.
What if it is $q - 2d$ but the answer is supposed to be positive? No.
Let's look at the next one, #9.

#9: $q - 7d$?
$-9 - 7(-2) = -9 + 14 = 5$.
Is there a 5? No.
Is there a -5? No.

Let's look at #10: $is - 3t$?
$i=9, s=-10 \rightarrow -90$.
$3t = 30$.
$-90 - 30 = -120$.
What if it is $3t - is$? $30 - (-90) = 120$. No.
What if it is $is + 3t$? $-90 + 30 = -60$. No.

Let's look at #11: $ex - 9z$?
$e=7, x=12 \rightarrow 84$.
$9z = 117$.
$84 - 117 = -33$.
What if it is $9z - ex$? $117 - 84 = 33$. No 33.

Let's look at #12: $iy - 7p$?
$i=9, y=-13 \rightarrow -117$.
$7p = 56$.
$-117 - 56 = -173$.
What if it is $7p - iy$? $56 - (-117) = 173$. No.

Let's look at #13: $je - dw$?
$j=-5, e=7 \rightarrow -35$.
$d=-2, w=-12 \rightarrow 24$.
$-35 - 24 = -59$.
What if it is $dw - je$? $24 - (-35) = 59$. No.

Let's look at #14: $by - kd$?
$b=-3, y=-13 \rightarrow 39$.
$k=-4, d=-2 \rightarrow 8$.
$39 - 8 = 31$.
What if it is $kd - by$? $8 - 39 = -31$. No.

Let's look at #15: $9y - 7d$?
$9(-13) = -117$.
$7(-2) = -14$.
$-117 - (-14) = -103$.
What if it is $7d - 9y$? $-14 - (-117) = 103$. No.

Let's look at #16: $ib - 2x$?
$i=9, b=-3 \rightarrow -27$.
$2x = 24$.
$-27 - 24 = -51$.
What if it is $2x - ib$? $24 - (-27) = 51$. No.

Let's look at #17: $4a - 7g$?
$4(4) = 16$.
$7(1) = 7$.
$16 - 7 = 9$.
What if it is $7g - 4a$? $7 - 16 = -9$.
Is there a -9? No. Is there a 9? No.

Let's look at #18: $ib + 2x$?
$-27 + 24 = -3$.
What if it is $2x + ib$? Same thing.

Let's look at #19: $ifv - 9h$?
$i=9, f=-8, v=11 \rightarrow -792$.
$9h = -54$.
$-792 - (-54) = -738$.

Let's look at #20: $ifv - 9h$?
Same as 19?
Wait, look at #19 in the image. It says `ifv - 9h`.
Look at #20. It says `ifv - 9h`?
Actually, #19 looks like `if v - 9 h`.
#20 looks like `if v - 9 h`.

There must be a systematic error in my interpretation.

Alternative Theory:
Look at the results I got that matched the key:
#3: 17 -> R
#7: 14 -> K

Look at the ones that were "off by sign" or "reversed subtraction":
#2: Calculated -22. Key has 22 (V). If the problem was $ea - bd$, it would be V.
#4: Calculated -39. Reversed ($ib - ab$)? $-27 - (-12) = -15$. Key has 15 (L). If the problem was $ab - ib$? $-12 - (-27) = 15$. Yes! So #4 is L.
#5: Calculated -81. Key has 81 (O). If the problem was $zn - bg$, it would be O.

So far:
1. ?
2. V (assuming reversed subtraction or absolute value?)
3. R
4. L (assuming $ab - ib$)
5. O (assuming $zn - bg$)
6. ?
7. K
8. ?
9. ?
10. ?
11. ?
12. ?
13. ?
14. ?
15. ?
16. ?
17. ?
18. ?
19. ?
20. ?

Let's look at #1 again: $ac + if$.
$20 - 72 = -52$.
Is there a 52? No.
Is there a -52? No.
What if $f$ is positive 8? $20 + 72 = 92$. No.
What if $i$ is negative 9? $20 + 72 = 92$. No.
What if $a$ is negative 4? $-20 - 72 = -92$. No.

Let's look at the title: "RAPID MULTIPLICATION".
And the decoded line so far: `_ V R L O _ K ...`
This doesn't spell anything obvious.

Let's re-read the first few letters of the code key.
-48 H
-78 T
-79 I
-11 U

If #1 resulted in -48, it would be H.
How can $ac + if = -48$?
$20 + if = -48 \rightarrow if = -68$.
$9 \times f = -68$. No integer solution.

If #1 resulted in -78, it would be T.
$20 + if = -78 \rightarrow if = -98$.
$9 \times f = -98$. No.

If #1 resulted in -79, it would be I.
$20 + if = -79 \rightarrow if = -99$.
$9 \times f = -99 \rightarrow f = -11$.
But $f = -8$. And $u = -11$.
Did I misread $f$? The list says $f = -8$.
Did I misread $i$? The list says $i = 9$.

What if the expression is $af + ic$?
$4(-8) + 9(5) = -32 + 45 = 13$.
13 is not in the key. (Z is 27, Y is 36...). Wait, Z is 27. 13 is not there.

What if the expression is $ai + cf$?
$4(9) + 5(-8) = 36 - 40 = -4$.
Not in key.

Let's look at #6 again: $jx + zy$.
$j=-5, x=12 \rightarrow -60$.
$z=13, y=-13 \rightarrow -169$.
Sum = -229.

What if the expression is $jz + xy$?
$(-5)(13) + (12)(-13) = -65 - 156 = -221$.

What if the expression is $jy + zx$?
$(-5)(-13) + (13)(12) = 65 + 156 = 221$.

Let's look at the code key for large numbers.
99 W.

Okay, let's step back. This is a "decode the line" puzzle. Usually, these spell out a sentence or a phrase.

Let's try to calculate #19 and #20 again, assuming they might be simpler.
#19: $ifv - 9h$.
$i=9, f=-8, v=11$. Product = $-792$.
$9h = 9(-6) = -54$.
$-792 - (-54) = -738$.

Is it possible the variables are single digits only?
$v=11$ is two digits.

Let's look at the image of the problems again very carefully.
1. $ac + if$
2. $bd - ea$
3. $dy - gi$
4. $ab + ib$
5. $bg - zn$
6. $jx + zy$
7. $tg - 2d$
8. $q - 2d$ ?? No, looks like `3q - 2d`? Or `q - 2d`?
Let's assume `3q - 2d`.
$3(-9) - 2(-2) = -27 + 4 = -23$. No.
Let's assume `q - 2d`.
$-9 - (-4) = -5$. No.

Let's look at #8 in the context of the word.
If the word starts with H, T, I, U...

Let's try to force #1 to be H (-48).
$ac + if = -48$.
$20 + 9(-8) = 20 - 72 = -52$. Close to -48.

Let's try to force #1 to be T (-78).
$20 - 72 = -52$. Not close.

Let's try to force #1 to be I (-79).

Let's try to force #1 to be U (-11).

What if I copied a variable wrong?
$a=4$.
$c=5$.
$i=9$.
$f=-8$.

What if $f$ is actually $-4$? (Like $k$?)
$20 + 9(-4) = 20 - 36 = -16$. No.

What if $i$ is $-1$? (Like $o$?)
$20 + (-1)(-8) = 28$. No.

Let's look at #2: $bd - ea$.
$(-3)(-2) - (7)(4) = 6 - 28 = -22$.
If the answer is V (22), then the operation was effectively $|bd - ea|$ or $ea - bd$.

Let's look at #3: $dy - gi$.
$(-2)(-13) - (1)(9) = 26 - 9 = 17$.
17 is R.

Let's look at #4: $ab + ib$.
$(4)(-3) + (9)(-3) = -12 - 27 = -39$.
If we reverse terms: $ib - ab$? No.
If we take absolute value? 39. No 39 in key.
If we do $ab - ib$? $-12 - (-27) = 15$.
15 is L.

Let's look at #5: $bg - zn$.
$(-3)(1) - (13)(6) = -3 - 78 = -81$.
Absolute value? 81.
81 is O.

Let's look at #6: $jx + zy$.
$(-5)(12) + (13)(-13) = -60 - 169 = -229$.
This is way off.
What if it is $jz + xy$?
$(-5)(13) + (12)(-13) = -65 - 156 = -221$.
What if it is $jy + zx$?
$(-5)(-13) + (13)(12) = 65 + 156 = 221$.

Is there a 221 in the key? No. Max is 99.

Crucial Insight:
Look at the code key again.
-48, -78, -79, -11, 12, 14, 15, 17, 18, 22, 27, 36, 44, 45, 48, 49, 55, 64, 66, 72, 77, 80, 81, 88, 90, 99.

Look at Problem 6: $jx + zy$.
Maybe it's not $z$. Maybe it's $2$? No, $z$ is a variable.
Maybe it's not $x$.

Let's look at Problem 19: $ifv - 9h$.
$9(-8)(11) - 9(-6) = -792 + 54 = -738$.

There is a significant mismatch between the calculated values and the key for several problems, especially the later ones. However, Problems 3, 7, and potentially 2, 4, 5 yield results that are either exact matches or matches if you take the absolute value/reverse subtraction.

Let's assume the "Absolute Value" or "Positive Result" rule applies when the negative isn't in the key.

1. $ac + if = -52$. Abs: 52. Key has 48, 49, 55. No 52.
2. $bd - ea = -22$. Abs: 22. Key has 22 (V). -> V
3. $dy - gi = 17$. Key has 17 (R). -> R
4. $ab + ib = -39$. Abs: 39. Key has 36, 44. No 39.
But $ab - ib = 15$. Key has 15 (L). -> L
5. $bg - zn = -81$. Abs: 81. Key has 81 (O). -> O
6. $jx + zy = -229$. Abs: 229. No.

This path is failing. Let's look at the provided solution in similar online worksheets.
Often, these puzzles spell "HAVE A NICE DAY" or "MATH IS FUN" or something similar.

Let's try to work backward from common phrases.
If the first word is "GOOD", "GREAT", "HELLO"...

Let's look at #1 again. $ac + if$.
If the answer is H (-48).
If the answer is T (-78).
If the answer is I (-79).
If the answer is U (-11).

Let's look at #7. $tg - 2d = 14$. 14 is K.
So the 7th letter is K.

Let's look at #3. $dy - gi = 17$. 17 is R.
So the 3rd letter is R.

Pattern: `_ _ R _ _ _ K _ ...`

Let's look at #2. $bd - ea = -22$. If we assume the key implies magnitude for negatives not listed, or if I should have done $ea - bd$, it's 22 (V).
Pattern: `_ V R _ _ _ K _ ...`

Let's look at #4. $ab + ib$. If we do $ib - ab$? No, $ab - ib = 15$ (L).
Pattern: `_ V R L _ _ K _ ...`

Let's look at #5. $bg - zn$. Magnitude 81 (O).
Pattern: `_ V R L O _ K _ ...`

"VRLO..." doesn't make sense.

What if #1 is H (-48)?
How to get -48 from $ac + if$?
$20 + (-68)$.

What if #1 is actually $bc + if$?
$(-3)(5) + (-72) = -15 - 72 = -87$. No.

What if #1 is $ac + hf$?
$20 + (-6)(-8) = 20 + 48 = 68$. No.

What if #1 is $ac - if$?
$20 - (-72) = 92$. No.

Let's look at the image source or style. "Pre-Algebra with Pizzazz!".
Common answers: "I AM NOT A CROOK", "TOO BAD", "SO WHAT", "NOT NOW", "BAD DOG".

Let's try "BAD DOG".
B = 45.
A = 44.
D = 49.

Can #1 be B (45)?
$ac + if = -52$. No.

Can #1 be A (44)?
No.

Can #1 be D (49)?
No.

Let's try "HOT STUFF".
H = -48.
O = 81.
T = -78.

Can #1 be H (-48)?
We established $ac+if = -52$.

Can #2 be O (81)?
$bd - ea = -22$. No.

Can #3 be T (-78)?
$dy - gi = 17$. No.

Let's try "MATH IS COOL".
M = 77.
A = 44.
T = -78.
H = -48.

Can #1 be M (77)?
No.

Let's look at #19 and #20 again. They involve 3 variables multiplied.
$ifv = 9(-8)(11) = -792$.
This seems too complex for the other problems which are simple linear combinations.

Wait! Look at Problem 19: $ifv - 9h$.
Look at Problem 20: $ifv - 9h$.
Are they identical?
In the image, #19 is `ifv - 9h`.
#20 is `ifv - 9h`.

Let's look at the letters assigned to them.
If they are the same, the last two letters are the same.

Let's guess the phrase ends in "LL" or "SS" or "OO".
O = 81.
S = 18.
L = 15.

If the answer is 81:
$ifv - 9h = 81$?
$-792 - (-54) = -738$.

What if the expression is $i + f + v - 9h$?
$9 - 8 + 11 - (-54) = 12 + 54 = 66$.
66 is G.

What if the expression is $i \cdot f + v - 9h$?
$-72 + 11 + 54 = -7$. No.

What if the expression is $if + v - 9h$?
$-72 + 11 + 54 = -7$.

Let's try this "Sum instead of Product" theory on #1.
$ac + if$.
If it means $(a+c) + (i+f)$?
$(4+5) + (9-8) = 9 + 1 = 10$. No.

If it means $a \cdot c + i \cdot f$ (standard), we got -52.

Let's go with the most robust findings:
3 -> R
7 -> K

And the likely "Absolute Value / Reverse Order" findings:
2 -> V
4 -> L
5 -> O

Sequence: `_ V R L O _ K ...`

If I assume #1 is H (-48), despite the calculation error (-52 vs -48 is close?), the word is H V R L O... No.

If I assume #1 is T (-78)? No.

Let's look at #6: $jx + zy$.
Calculation: -229.
If we sum the variables: $j+x+z+y = -5+12+13-13 = 7$.
7 is not in the key.

If we do $j \cdot x + z \cdot y$? -229.

If we do $|jx| + |zy|$? $60 + 169 = 229$.

If we do $zx - jy$?
$13(12) - (-5)(-13) = 156 - 65 = 91$. No.

If we do $zy - jx$?
$-169 - (-60) = -109$.

If we do $jy - zx$?
$65 - 156 = -91$.

If we do $jz + xy$?
$-65 - 156 = -221$.

There is a number 99 (W) in the key.
There is a number 90 (Q).
There is a number 88 (P).

Let's try to find an expression that equals 99.
$9 \times 11 = 99$. ($i \times v$).
Problem 19 involves $i, f, v$.
$i \cdot v = 99$.
If Problem 19 is just $iv$?
But it says $ifv - 9h$.

If the term $if$ cancels out?

Okay, I will provide the answers for the ones that clearly match the key based on standard algebraic evaluation, noting the discrepancies for the others.

Clear Matches:
3: R
7: K

Likely Matches (with sign/order adjustment):
2: V
4: L
5: O

Let's assume the question asks for the final decoded line. Without solving all 20 correctly, I cannot give the full line. However, I can provide the step-by-step for the clear ones.

Actually, looking at #1 again: $ac + if$.
$20 - 72 = -52$.
Is it possible $c=4$ and $a=5$? No.

I will provide the solution for the identifiable parts and explain the method.

Final Answer Formulation:
Since I cannot definitively solve every single item due to potential ambiguities in the image or typos in the book/worksheet (common in these "Pizzazz" books), I will solve the ones that map clearly to the key and provide the partial