Let's solve both problems step by step.
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Problem #15
Problem Statement:
Sarah has "$D" dollars. If she had $50 more, she would have $120. Write and solve an equation to determine the amount of money Sarah has.
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Step 1: Define the variable
Let $ D $ = the amount of money Sarah currently has.
Step 2: Set up the equation
If she had $50 more, she would have $120:
$$
D + 50 = 120
$$
Step 3: Solve for $ D $
Subtract 50 from both sides:
$$
D = 120 - 50 = 70
$$
Answer:
Sarah has
$70.
---
Problem #16
Problem Statement:
Three friends competed in a race. Their score comes from their total time. The first person completed the race in $ \frac{3}{4} $ of an hour, the second finished in $ 1\frac{1}{2} $ hours, and the third finished in $ 2\frac{1}{2} $ hours. What is the time difference between the first finisher and the last?
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Step 1: Convert all times to improper fractions or decimals for easier calculation.
- First finisher: $ \frac{3}{4} $ hour = $ 0.75 $ hours
- Second finisher: $ 1\frac{1}{2} = 1 + \frac{1}{2} = 1.5 $ hours
- Third finisher (last): $ 2\frac{1}{2} = 2 + \frac{1}{2} = 2.5 $ hours
Step 2: Find the time difference between the first and last finishers
$$
\text{Difference} = \text{Last} - \text{First} = 2.5 - 0.75 = 1.75 \text{ hours}
$$
Convert 1.75 hours to a mixed number:
$$
1.75 = 1 \frac{3}{4} \text{ hours}
$$
Or as a fraction:
$$
1.75 = \frac{7}{4} \text{ hours}
$$
Answer:
The time difference between the first and last finisher is
$ 1\frac{3}{4} $ hours (or $ \frac{7}{4} $ hours).
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✔ Final Answers:
-
Problem #15: Sarah has
$70.
-
Problem #16: The time difference is
$ 1\frac{3}{4} $ hours.
Parent Tip: Review the logic above to help your child master the concept of middle school math problem solving worksheet.
