Linear Equations Word Problems Worksheets with Answer Key - Free Printable

Let's solve each problem step by step.

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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:

- David’s rate = $ \frac{1}{3} $ of the room per hour
- Sara’s rate = $ \frac{1}{6} $ of the room per hour

Together, their combined rate:
$$
\frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}
$$

So together, they paint $ \frac{1}{2} $ of the room per hour.

Time to paint the whole room:
$$
\frac{1}{\frac{1}{2}} = 2 \text{ hours}
$$

✔ Answer: 2 hours

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

Simplify:
$$
2x + x + 2 + 3x + 12 = 152 \\
6x + 14 = 152
$$

Subtract 14 from both sides:
$$
6x = 138
$$

Divide by 6:
$$
x = 23
$$

So the numbers are:
- First: 23
- Second: 25
- Third: 27

Check:
$$
2(23) + 25 + 3(27) = 46 + 25 + 81 = 152 \quad \text{✓}
$$

✔ Answer: 23, 25, 27

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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 the cost of one candy bar be $ x $.

Total cost:
$$
4 + 8x = 28
$$

Subtract 4:
$$
8x = 24
$$

Divide by 8:
$$
x = 3
$$

✔ Answer: Each candy bar costs $3.

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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 = 4 m
- Width = 2 m

Perimeter:
$$
P = 2(l + w) = 2(4 + 2) = 2(6) = 12 \text{ m}
$$

Now, width becomes 5 m, perimeter remains 12 m.

Let new length be $ l $.

$$
2(l + 5) = 12 \\
l + 5 = 6 \\
l = 1
$$

✔ Answer: New length is 1 meter

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

Solution:

Each watermelon costs $1.

Number she can buy:
$$
\frac{11}{1} = 11
$$

✔ Answer: 11 watermelons

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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

✔ Answer: The smallest number is 50

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✔ Final Answers:

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

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