Linear Equations Word Problems Worksheet featuring six real-world math scenarios to solve.

Let’s solve each problem one by one, with clear explanations.

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Problem 1:

> David takes 3 hrs to paint a room. Sara takes 6 hrs to complete the same job. If they work together how long will they take to complete the task?

Solution:

This is a work rate problem.

- David’s rate = 1 room / 3 hours = 1/3 rooms per hour.
- Sara’s rate = 1 room / 6 hours = 1/6 rooms per hour.

Combined rate = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 rooms per hour.

So, together they paint half a room per hour, meaning it takes them 2 hours to paint the whole room.

✔ Answer: 2 hours

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Problem 2:

> Find three consecutive odd integers such that the sum of twice the first, the second and three times the third is 152.

Solution:

Let the three consecutive odd integers be:

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

According to the problem:

> 2*(first) + (second) + 3*(third) = 152

Substitute:

2x + (x + 2) + 3(x + 4) = 152

Simplify:

2x + x + 2 + 3x + 12 = 152
→ 6x + 14 = 152
→ 6x = 138
→ x = 23

So the numbers are: 23, 25, 27

Check:
2*23 = 46
+ 25 = 71
+ 3*27 = 81 → 71 + 81 = 152 ✔

✔ Answer: 23, 25, 27

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Problem 3:

> Nancy bought a soft drink for $4 and 8 candy bars. She spent a total of $28. How much did each candy bar cost?

Solution:

Let cost of each candy bar = x dollars.

Total cost = soft drink + 8 candy bars = 4 + 8x = 28

Solve:

8x = 28 - 4 = 24
x = 24 / 8 = 3

✔ Answer: $3 per candy bar

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Problem 4:

> A rectangle is 2 m tall and 4 m wide. If its width is enlarged to 5 m without changing its perimeter, then find the new length of the rectangle?

Solution:

Original dimensions:
Length (L) = 4 m, Width (W) = 2 m
Perimeter = 2(L + W) = 2(4 + 2) = 2 * 6 = 12 meters

New width = 5 m
Let new length = x meters
Perimeter remains 12 m:

2(x + 5) = 12
→ x + 5 = 6
→ x = 1

✔ Answer: 1 meter

*(Note: “Tall” usually means height/width, “wide” means length — but in rectangles, we just use length and width. The problem says “2m tall and 4m wide”, so we assume width=2m, length=4m. When width becomes 5m, length must shrink to keep perimeter same.)*

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Problem 5:

> Mary bought one seedless watermelon for $1. How many seedless watermelons can she buy for $11?

Solution:

If 1 watermelon costs $1, then for $11, she can buy:

11 ÷ 1 = 11 watermelons

✔ Answer: 11

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Problem 6:

> The sum of three consecutive even numbers is 156. What is the smallest number?

Solution:

Let the three consecutive even numbers be:

- x
- x + 2
- x + 4

Sum: x + (x+2) + (x+4) = 156
→ 3x + 6 = 156
→ 3x = 150
→ x = 50

So the numbers are 50, 52, 54 → smallest is 50

✔ Answer: 50

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✔ Final Answers:

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

Let me know if you’d like these written out on the worksheet format!