Student holds a math worksheet featuring a "Double Cross" algebra puzzle with riddles and variable expressions.
A person holding a worksheet titled "Double Cross" with algebraic expressions and a riddle involving a porcupine and a gopher, and a pelican and a lightning bolt, with values to decode the answers.
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Step-by-step solution for: a DOUBLE CROSS 1. What do you get when you cross a porcupine with ...
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Show Answer Key & Explanations
Step-by-step solution for: a DOUBLE CROSS 1. What do you get when you cross a porcupine with ...
Let’s solve this step by step.
We are told to use these values:
- a = 1
- b = 2
- c = 3
- w = 0
- x = 10
- y = 6
We need to evaluate each expression and match the result to the numbers in the code lines for questions 1 and 2. Then we write the letter above each number that matches.
---
First, let’s compute all the expressions one by one.
Left column:
(H) xy
= 10 × 6 = 60
(A) b + (cy)
= 2 + (3 × 6) = 2 + 18 = 20
(W) x - (ac)
= 10 - (1 × 3) = 10 - 3 = 7
(S) (7b) + (4c)
= (7×2) + (4×3) = 14 + 12 = 26
(E) (8x) - (3y)
= (8×10) - (3×6) = 80 - 18 = 62
(U) (ax) + (by)
= (1×10) + (2×6) = 10 + 12 = 22
(B) (2x) · (b + c)
= (2×10) × (2 + 3) = 20 × 5 = 100
(G) (x + y)/(c - a)
= (10 + 6)/(3 - 1) = 16/2 = 8
---
Right column:
(R) (xy)/(x + b)
= (10×6)/(10 + 2) = 60/12 = 5
(T) (wa)/b
= (0×1)/2 = 0/2 = 0
(K) (x - y)·(y - w)
= (10 - 6) × (6 - 0) = 4 × 6 = 24
(N) c·(y + c)·(y - c)
= 3 × (6 + 3) × (6 - 3) = 3 × 9 × 3 = 81
Wait — 3 × 9 = 27; 27 × 3 = 81
(C) (3x)/b · (abc)
First, (3x)/b = (3×10)/2 = 30/2 = 15
Then abc = 1×2×3 = 6
So 15 × 6 = 90
But wait — is it (3x)/b multiplied by (abc)? Yes, as written: “(3x)/b · (abc)” → so yes, 15 × 6 = 90.
(I) (8bc) - (w + x + y)
8bc = 8×2×3 = 48
w + x + y = 0 + 10 + 6 = 16
48 - 16 = 32
(L) (x - b)/(y + b)
= (10 - 2)/(6 + 2) = 8/8 = 1
---
Now let’s list all results with their letters:
- H → 60
- A → 20
- W → 7
- S → 26
- E → 62
- U → 22
- B → 100
- G → 8
- R → 5
- T → 0
- K → 24
- N → 81
- C → 90
- I → 32
- L → 1
Also note: We have two more? Wait, let’s check if we missed any.
Looking back at the image layout — there are 15 total expressions? Let me count:
Left: H, A, W, S, E, U, B, G → 8
Right: R, T, K, N, C, I, L → 7
Total 15 — correct.
Now, let’s decode Question 1:
Question 1 code:
20 0 22 81 81 62 1 7 32 0 60 1 62 20 24 26
Match each number to its letter:
20 → A
0 → T
22 → U
81 → N
81 → N
62 → E
1 → L
7 → W
32 → I
0 → T
60 → H
1 → L
62 → E
20 → A
24 → K
26 → S
So writing the letters in order:
A T U N N E L W I T H L E A K S
That spells: “ATUNNELWITHLEAKS” → probably meant to be “A tunnel with leaks”
But since it’s a joke answer, maybe it’s “a tunnel with leaks” — but let’s keep going.
Actually, looking again: The first word might be “A” then “tunnel” — but ATUNNEL isn’t right. Wait — perhaps it’s “A” + “tunnel” = “A tunnel”, but spelled without space.
Alternatively, maybe it’s “A” then “tunnel” — but let’s see the second question too.
Wait — actually, let’s double-check the sequence:
Code for Q1:
20 → A
0 → T
22 → U
81 → N
81 → N
62 → E
1 → L
7 → W
32 → I
0 → T
60 → H
1 → L
62 → E
20 → A
24 → K
26 → S
So: A-T-U-N-N-E-L-W-I-T-H-L-E-A-K-S
Grouped: A TUNNEL WITH LEAKS → “A tunnel with leaks”
Yes! That makes sense.
Now Question 2:
Question 2 code:
20 100 32 8 62 1 62 90 0 5 32 90 100 32 1 1
Match:
20 → A
100 → B
32 → I
8 → G
62 → E
1 → L
62 → E
90 → C
0 → T
5 → R
32 → I
90 → C
100 → B
32 → I
1 → L
1 → L
So: A-B-I-G-E-L-E-C-T-R-I-C-B-I-L-L
Spell it out: ABIGELECTRICBILL → Hmm… not quite.
Wait — group properly:
A B I G E L E C T R I C B I L L
Try grouping: A BIG ELECTRIC BILL?
Let’s see:
Positions:
1: A
2: B
3: I
4: G → “BIG” starts here? But position 2 is B, 3 is I, 4 is G → “BIG”
Then 5: E
6: L
7: E → “ELE”? Not good.
Wait — after “BIG”, next is E, L, E, C, T, R, I, C → “ELECTRIC”
Then B, I, L, L → “BILL”
So: A + BIG + ELECTRIC + BILL → “A big electric bill”
Perfect!
So answers:
Q1: A tunnel with leaks
Q2: A big electric bill
But the worksheet says “write the letter of that exercise above it” — meaning we fill in the blanks with letters corresponding to the numbers.
For Q1: The blank line has underscores under each number. So we write the letter above each number.
Similarly for Q2.
But the final answer expected is likely the decoded phrases.
Since the user didn’t specify format, but based on context, they want the decoded jokes.
Final Answer:
1. A tunnel with leaks
2. A big electric bill
We are told to use these values:
- a = 1
- b = 2
- c = 3
- w = 0
- x = 10
- y = 6
We need to evaluate each expression and match the result to the numbers in the code lines for questions 1 and 2. Then we write the letter above each number that matches.
---
First, let’s compute all the expressions one by one.
Left column:
(H) xy
= 10 × 6 = 60
(A) b + (cy)
= 2 + (3 × 6) = 2 + 18 = 20
(W) x - (ac)
= 10 - (1 × 3) = 10 - 3 = 7
(S) (7b) + (4c)
= (7×2) + (4×3) = 14 + 12 = 26
(E) (8x) - (3y)
= (8×10) - (3×6) = 80 - 18 = 62
(U) (ax) + (by)
= (1×10) + (2×6) = 10 + 12 = 22
(B) (2x) · (b + c)
= (2×10) × (2 + 3) = 20 × 5 = 100
(G) (x + y)/(c - a)
= (10 + 6)/(3 - 1) = 16/2 = 8
---
Right column:
(R) (xy)/(x + b)
= (10×6)/(10 + 2) = 60/12 = 5
(T) (wa)/b
= (0×1)/2 = 0/2 = 0
(K) (x - y)·(y - w)
= (10 - 6) × (6 - 0) = 4 × 6 = 24
(N) c·(y + c)·(y - c)
= 3 × (6 + 3) × (6 - 3) = 3 × 9 × 3 = 81
Wait — 3 × 9 = 27; 27 × 3 = 81
(C) (3x)/b · (abc)
First, (3x)/b = (3×10)/2 = 30/2 = 15
Then abc = 1×2×3 = 6
So 15 × 6 = 90
But wait — is it (3x)/b multiplied by (abc)? Yes, as written: “(3x)/b · (abc)” → so yes, 15 × 6 = 90.
(I) (8bc) - (w + x + y)
8bc = 8×2×3 = 48
w + x + y = 0 + 10 + 6 = 16
48 - 16 = 32
(L) (x - b)/(y + b)
= (10 - 2)/(6 + 2) = 8/8 = 1
---
Now let’s list all results with their letters:
- H → 60
- A → 20
- W → 7
- S → 26
- E → 62
- U → 22
- B → 100
- G → 8
- R → 5
- T → 0
- K → 24
- N → 81
- C → 90
- I → 32
- L → 1
Also note: We have two more? Wait, let’s check if we missed any.
Looking back at the image layout — there are 15 total expressions? Let me count:
Left: H, A, W, S, E, U, B, G → 8
Right: R, T, K, N, C, I, L → 7
Total 15 — correct.
Now, let’s decode Question 1:
Question 1 code:
20 0 22 81 81 62 1 7 32 0 60 1 62 20 24 26
Match each number to its letter:
20 → A
0 → T
22 → U
81 → N
81 → N
62 → E
1 → L
7 → W
32 → I
0 → T
60 → H
1 → L
62 → E
20 → A
24 → K
26 → S
So writing the letters in order:
A T U N N E L W I T H L E A K S
That spells: “ATUNNELWITHLEAKS” → probably meant to be “A tunnel with leaks”
But since it’s a joke answer, maybe it’s “a tunnel with leaks” — but let’s keep going.
Actually, looking again: The first word might be “A” then “tunnel” — but ATUNNEL isn’t right. Wait — perhaps it’s “A” + “tunnel” = “A tunnel”, but spelled without space.
Alternatively, maybe it’s “A” then “tunnel” — but let’s see the second question too.
Wait — actually, let’s double-check the sequence:
Code for Q1:
20 → A
0 → T
22 → U
81 → N
81 → N
62 → E
1 → L
7 → W
32 → I
0 → T
60 → H
1 → L
62 → E
20 → A
24 → K
26 → S
So: A-T-U-N-N-E-L-W-I-T-H-L-E-A-K-S
Grouped: A TUNNEL WITH LEAKS → “A tunnel with leaks”
Yes! That makes sense.
Now Question 2:
Question 2 code:
20 100 32 8 62 1 62 90 0 5 32 90 100 32 1 1
Match:
20 → A
100 → B
32 → I
8 → G
62 → E
1 → L
62 → E
90 → C
0 → T
5 → R
32 → I
90 → C
100 → B
32 → I
1 → L
1 → L
So: A-B-I-G-E-L-E-C-T-R-I-C-B-I-L-L
Spell it out: ABIGELECTRICBILL → Hmm… not quite.
Wait — group properly:
A B I G E L E C T R I C B I L L
Try grouping: A BIG ELECTRIC BILL?
Let’s see:
Positions:
1: A
2: B
3: I
4: G → “BIG” starts here? But position 2 is B, 3 is I, 4 is G → “BIG”
Then 5: E
6: L
7: E → “ELE”? Not good.
Wait — after “BIG”, next is E, L, E, C, T, R, I, C → “ELECTRIC”
Then B, I, L, L → “BILL”
So: A + BIG + ELECTRIC + BILL → “A big electric bill”
Perfect!
So answers:
Q1: A tunnel with leaks
Q2: A big electric bill
But the worksheet says “write the letter of that exercise above it” — meaning we fill in the blanks with letters corresponding to the numbers.
For Q1: The blank line has underscores under each number. So we write the letter above each number.
Similarly for Q2.
But the final answer expected is likely the decoded phrases.
Since the user didn’t specify format, but based on context, they want the decoded jokes.
Final Answer:
1. A tunnel with leaks
2. A big electric bill
Parent Tip: Review the logic above to help your child master the concept of double cross worksheet.