Linear Equations Word Problems Worksheet featuring six practical math problems for students to solve.

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

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Problem 1:

David takes 3 hours to paint a room → So in 1 hour, he paints 1/3 of the room.
Sara takes 6 hours → So in 1 hour, she paints 1/6 of the room.

Together, in 1 hour, they paint:
→ 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 of the room.

So if together they paint half the room in 1 hour, then to paint the whole room, it will take them:
→ 2 hours.

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

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Problem 2:

We need three consecutive odd integers. Let’s call them:

First: x
Second: x + 2
Third: x + 4

The problem says:
“sum of twice the first, the second and three times the third is 152”

That means:
2×(first) + (second) + 3×(third) = 152
→ 2x + (x + 2) + 3(x + 4) = 152

Now simplify:
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: Twice first = 46, second = 25, three times third = 81 → 46 + 25 + 81 = 152 → Correct!

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Problem 3:

Nancy bought:
- 1 soft drink for $4
- 8 candy bars (each costs same amount — let’s say $c per bar)
Total spent: $28

Equation:
4 + 8c = 28

Subtract 4 from both sides:
8c = 24

Divide by 8:
c = 3

Each candy bar cost $3

✔ Check: 8 × 3 = 24, plus 4 = 28 → Correct!

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Problem 4:

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

New rectangle:
Width becomes 5 m, height changes to ? (let’s call it h), but perimeter stays 12 m.

So:
2×(h + 5) = 12

Divide both sides by 2:
h + 5 = 6

Subtract 5:
h = 1

Wait — the question asks for “new length”. But which side is length? Usually, length is the longer side. Originally, width was 4m, height 2m — so maybe “length” meant width? Or perhaps we should assume “length” refers to the horizontal side?

But after enlargement, width is now 5m, and new height is 1m. So if “length” means the longer dimension, then it’s still 5m? That doesn’t make sense because it didn’t change.

Wait — re-read: “If its width is enlarged to 5 m without changing its perimeter, then find the new length of the rectangle?”

Probably here, “length” means the other side — the vertical side (which was originally called “tall” = height). So they’re asking for the new height.

In that case, answer is 1 meter.

But let’s double-check wording: “A rectangle is 2 m tall and 4 m wide.” So tall = height, wide = width.

Then: “width is enlarged to 5 m” → new width = 5m. Perimeter unchanged → still 12m.

So: 2*(new_height + 5) = 12 → new_height = 1m.

They ask for “new length” — possibly meaning the new dimension that changed? Or maybe they mean the new value of the side that wasn't widened? Since "length" isn't clearly defined, but in context, since width changed, and they want the other side — it's likely they mean the new height.

Alternatively, maybe “length” refers to the longer side — but now 5m > 1m, so length would be 5m — but that didn’t change? No, width became 5m — so if length = width, then it’s 5m — but that’s given.

This is ambiguous — but looking at standard problems like this, when they say “find the new length”, and they changed the width, they usually mean the other dimension — the height.

Also, original “tall” was 2m — now it’s 1m — so probably answer is 1 meter.

✔ Check: New dimensions: 1m by 5m → perimeter = 2*(1+5)=12 → matches original → correct.

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Problem 5:

Mary bought 1 watermelon for $1 → so each costs $1.

How many can she buy for $11?

Simple division: 11 ÷ 1 = 11

✔ Check: 11 × $1 = $11 → correct.

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Problem 6:

Three consecutive even numbers. Let’s call them:

x, x+2, x+4

Sum = 156

So:
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