Let’s solve each equation one by one to find the value of
x. Then we’ll match that number to the code at the bottom to get letters and solve the riddle.
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We have 12 equations. Let’s go row by row, left column first (M, O, C, N, H, S), then right column (D, A, E, T, R, I).
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Left Column:
1.
M: x + 12 = 20
Subtract 12 from both sides:
x = 20 - 12 →
x = 8
2.
O: x - 9 = 12
Add 9 to both sides:
x = 12 + 9 →
x = 21
3.
C: 42 = 7x
Divide both sides by 7:
x = 42 ÷ 7 →
x = 6
4.
N: x/8 = 9
Multiply both sides by 8:
x = 9 × 8 →
x = 72
5.
H: 5 = x - 17
Add 17 to both sides:
x = 5 + 17 →
x = 22
6.
S: 3 = x/12
Multiply both sides by 12:
x = 3 × 12 →
x = 36
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Right Column:
7.
D: 3x = 21
Divide both sides by 3:
x = 21 ÷ 3 →
x = 7
8.
A: x/5 = 6
Multiply both sides by 5:
x = 6 × 5 →
x = 30
9.
E: x - 13 = 11
Add 13 to both sides:
x = 11 + 13 →
x = 24
10.
T: x + 18 = 49
Subtract 18 from both sides:
x = 49 - 18 →
x = 31
11.
R: 4x = 52
Divide both sides by 4:
x = 52 ÷ 4 →
x = 13
12.
I: 29 = x + 13
Subtract 13 from both sides:
x = 29 - 13 →
x = 16
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Now let’s list all solutions with their corresponding letters:
- M → 8
- O → 21
- C → 6
- N → 72
- H → 22
- S → 36
- D → 7
- A → 30
- E → 24
- T → 31
- R → 13
- I → 16
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Now look at the code at the bottom:
> WHY DIDN’T THE QUARTER ROLL DOWN THE HILL WITH THE NICKEL?
> Code numbers:
> 16 31 22 30 7 8 21 13 24 6 24 72 31 36
Let’s match each number to its letter:
- 16 → I
- 31 → T
- 22 → H
- 30 → A
- 7 → D
- 8 → M
- 21 → O
- 13 → R
- 24 → E
- 6 → C
- 24 → E
- 72 → N
- 31 → T
- 36 → S
So putting it together:
I T H A D M O R E C E N T S
Wait — that doesn’t make sense. Let’s group them properly as words.
Looking again:
The phrase is: “WHY DIDN’T THE QUARTER ROLL DOWN THE HILL WITH THE NICKEL?”
And the answer should be a pun or joke.
Our decoded letters in order:
16 → I
31 → T
22 → H
30 → A
7 → D
8 → M
21 → O
13 → R
24 → E
6 → C
24 → E
72 → N
31 → T
36 → S
So:
I T H A D M O R E C E N T S
That spells:
“IT HAD MORE CENTS”
Ah! That makes sense!
Because a quarter is worth 25 cents, and a nickel is 5 cents — so the quarter had more cents… and that’s why it didn’t roll down? Wait — actually, the joke is probably playing on “cents” vs “sense”.
But according to our decoding, the answer is:
“IT HAD MORE CENTS”
Which is a play on words — “more sense” but written as “more cents” because we’re talking about coins.
Perfect!
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Final Answer:
IT HAD MORE CENTS
Parent Tip: Review the logic above to help your child master the concept of one step algebraic equations worksheet.
