Linear Equations Word Problems Worksheets with Answer Key - Free Printable

Let’s solve each problem one by one, step by step.

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Problem 1: David and Sara painting together

David takes 3 hours → so in 1 hour, he does 1/3 of the job.
Sara takes 6 hours → so in 1 hour, she does 1/6 of the job.

Together in 1 hour:
1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 of the job.

So they do half the job in 1 hour → full job in 2 hours.

✔ Check: In 2 hours, David does 2 × (1/3) = 2/3. Sara does 2 × (1/6) = 1/3. Total = 2/3 + 1/3 = 1 → correct.

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Problem 2: Three consecutive odd integers

Let the first odd integer be x.
Then next two are x+2 and x+4 (since odd numbers go up by 2).

Given:
Twice the first + second + three times the third = 152
→ 2(x) + (x+2) + 3(x+4) = 152

Expand:
2x + x + 2 + 3x + 12 = 152
Combine like terms:
(2x + x + 3x) + (2 + 12) = 152
6x + 14 = 152

Subtract 14 from both sides:
6x = 138

Divide by 6:
x = 23

So the numbers are:
23, 25, 27

✔ Check:
2×23 = 46
+25 = 71
+3×27 = 81 → 71 + 81 = 152 → correct.

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Problem 3: Nancy’s candy bars

She bought:
- 1 soft drink for $4
- 8 candy bars (let cost per bar = c)
Total spent = $28

Equation:
4 + 8c = 28

Subtract 4:
8c = 24

Divide by 8:
c = 3

Each candy bar costs $3

✔ Check: 8 × 3 = 24 + 4 = 28 → correct.

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Problem 4: Rectangle perimeter unchanged

Original rectangle:
Height = 2 m, Width = 4 m
Perimeter = 2×(height + width) = 2×(2+4) = 2×6 = 12 m

New width = 5 m, height becomes unknown → let new height = h
Perimeter still 12 m → 2×(h + 5) = 12

Divide both sides by 2:
h + 5 = 6

Subtract 5:
h = 1

New length (height) is 1 meter

✔ Check: 2×(1 + 5) = 2×6 = 12 → same as before → correct.

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Problem 5: Watermelons for $11

One watermelon = $1
How many for $11? → Just divide: 11 ÷ 1 = 11

✔ Simple check: 11 × $1 = $11 → correct.

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Problem 6: Three consecutive even numbers sum to 156

Let smallest even number = x
Next two: x+2, x+4

Sum: x + (x+2) + (x+4) = 156
→ 3x + 6 = 156

Subtract 6:
3x = 150

Divide by 3:
x = 50

Smallest number is 50

✔ Check: 50 + 52 + 54 = 156 → correct.

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Final Answer:
1. 2 hours
2. 23, 25, 27
3. $3
4. 1 meter
5. 11
6. 50