Algebra worksheet with "Tom Swifty" jokes where solving algebra problems reveals missing words to complete the punchlines.

This is a fun “Tom Swifty” algebra puzzle! We need to solve each word problem algebraically, match the solution (the number) to the corresponding letter code above, and then fill in the missing words for Tom’s quotes.

Let’s go step-by-step.

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## Step 1: Solve each algebra problem

We’ll label each problem with its letter and solve it.

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D. Seven times a number is the same as 12 more than 3 times the number. Find the number.

Let the number = `x`

Equation:
`7x = 3x + 12`

Subtract 3x from both sides:
`4x = 12`

Divide by 4:
x = 3

→ Letter D → 3

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E. Six more than 5 times a number is the same as 9 less than twice the number. Find the number.

Let the number = `x`

Equation:
`5x + 6 = 2x - 9`

Subtract 2x from both sides:
`3x + 6 = -9`

Subtract 6:
`3x = -15`

Divide by 3:
x = -5

→ Letter E → -5

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U. Three less than 11 times a number is the same as the number decreased by 13. Find the number.

Equation:
`11x - 3 = x - 13`

Subtract x:
`10x - 3 = -13`

Add 3:
`10x = -10`

Divide by 10:
x = -1

→ Letter U → -1

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C. One more than 3 times a number is the same as 5 times the number, decreased by 15. Find the number.

Equation:
`3x + 1 = 5x - 15`

Subtract 3x:
`1 = 2x - 15`

Add 15:
`16 = 2x`

Divide by 2:
x = 8

→ Letter C → 8

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Y. Twelve less than a number is the same as 6, decreased by 8 times the number. Find the number.

Equation:
`x - 12 = 6 - 8x`

Add 8x to both sides:
`9x - 12 = 6`

Add 12:
`9x = 18`

Divide by 9:
x = 2

→ Letter Y → 2

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W. Ten increased by 6 times a number is the same as 4 less than 4 times the number. Find the number.

Equation:
`6x + 10 = 4x - 4`

Subtract 4x:
`2x + 10 = -4`

Subtract 10:
`2x = -14`

Divide by 2:
x = -7

→ Letter W → -7

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I. Eight times a number plus 3 times the number is the same as 9 more than 12 times the number. Find the number.

Equation:
`8x + 3x = 12x + 9`

Simplify left:
`11x = 12x + 9`

Subtract 12x:
`-x = 9`

Multiply by -1:
x = -9

→ Letter I → -9

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K. The sum of two numbers is 35. Three times the larger number is the same as 4 times the smaller number. Find the larger number.

Let larger number = `x`, smaller = `35 - x`

Equation:
`3x = 4(35 - x)`

Expand right:
`3x = 140 - 4x`

Add 4x:
`7x = 140`

Divide by 7:
x = 20

→ Letter K → 20

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T. The sum of two numbers is 24. Seven times the smaller number is the same as 5 times the larger number. Find the smaller number.

Let smaller = `x`, larger = `24 - x`

Equation:
`7x = 5(24 - x)`

Expand:
`7x = 120 - 5x`

Add 5x:
`12x = 120`

Divide by 12:
x = 10

→ Letter T → 10

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F. An orange has 20 fewer calories than a banana. If 7 bananas have the same number of calories as 9 oranges, how many calories are in a banana?

Let banana calories = `b`, orange = `b - 20`

Equation:
`7b = 9(b - 20)`

Expand:
`7b = 9b - 180`

Subtract 9b:
`-2b = -180`

Divide by -2:
b = 90

→ Letter F → 90

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L. Keith weighs 20 kg more than Beth, while Henry weighs 30 kg less than twice as much as Beth. If Keith and Henry weigh the same, how much does Beth weigh (in kg)?

Let Beth = `b`

Keith = `b + 20`
Henry = `2b - 30`

Set equal:
`b + 20 = 2b - 30`

Subtract b:
`20 = b - 30`

Add 30:
b = 50

→ Letter L → 50

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N. Cycle Paths, Inc. makes bicycles, tricycles, and unicycles. Last week they made 88 more bicycles than unicycles, and 5 times as many tricycles as unicycles. If they made 40 more bicycles than tricycles, how many unicycles did they make?

Let unicycles = `u`

Bicycles = `u + 88`
Tricycles = `5u`

Also: Bicycles = Tricycles + 40 → `u + 88 = 5u + 40`

Solve:
`u + 88 = 5u + 40`

Subtract u:
`88 = 4u + 40`

Subtract 40:
`48 = 4u`

Divide by 4:
u = 12

→ Letter N → 12

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## Step 2: Match solutions to the code above each quote

We now have:

| Letter | Solution |
|--------|--------|
| D | 3 |
| E | -5 |
| U | -1 |
| C | 8 |
| Y | 2 |
| W | -7 |
| I | -9 |
| K | 20 |
| T | 10 |
| F | 90 |
| L | 50 |
| N | 12 |

Now look at the three quotes and their number sequences.

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## Quote 1: “I love to go camping,” Tom said

Numbers:
`-9 12 10 -5 12 10 50 2`

Match to letters:

- -9 → I
- 12 → N
- 10 → T
- -5 → E
- 12 → N
- 10 → T
- 50 → L
- 2 → Y

So: I N T E N T L Y

→ “I love to go camping,” Tom said intently

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## Quote 2: “I think I’m sick,” Tom said

Numbers:
`90 50 -1 -5 12 10 50 2`

Match:

- 90 → F
- 50 → L
- -1 → U
- -5 → E
- 12 → N
- 10 → T
- 50 → L
- 2 → Y

→ F L U E N T L Y

→ “I think I’m sick,” Tom said fluently

*(Note: “fluently” is a bit odd for being sick — maybe a pun? But mathematically correct.)*

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## Quote 3: “Light the fuse,” Tom said

Numbers:
`-7 -9 8 20 -5 3 50 2`

Match:

- -7 → W
- -9 → I
- 8 → C
- 20 → K
- -5 → E
- 3 → D
- 50 → L
- 2 → Y

→ W I C K E D L Y

→ “Light the fuse,” Tom said wickedly

*(Perfect pun — lighting a fuse wickedly implies mischief or danger.)*

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## ✔ Final Answer:

1. “I love to go camping,” Tom said *intently*.
2. “I think I’m sick,” Tom said *fluently*.
3. “Light the fuse,” Tom said *wickedly*.

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## 📝 Note:
“Fluently” for “I think I’m sick” is a stretch — perhaps it's meant to be humorous or ironic (like saying it fluently despite being sick). In some versions of this worksheet, the second quote might be intended to say “*feebly*” or “*faintly*”, but according to our algebra, the only matching word is “fluently”.

Double-checking the math — all equations are solved correctly. So we must accept “fluently” as the decoded word.

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✔ All problems solved algebraically, decoded successfully!