Ratio Word Problems - Algebra 1 - Free Printable

Let's solve both ratio word problems step by step.

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Problem 1:

The ratio of boys to girls in a school is 11:10. If there are 525 students in the school, how many are boys?

#### Step 1: Understand the ratio
- The ratio of boys to girls is 11:10, meaning for every 11 boys, there are 10 girls.
- Total parts = 11 (boys) + 10 (girls) = 21 parts

#### Step 2: Find value of one part
- Total students = 525
- So, each part represents:
$$
\frac{525}{21} = 25
$$

#### Step 3: Calculate number of boys
- Boys = 11 parts × 25 =
$$
11 \times 25 = 275
$$

✔ Answer: There are 275 boys.

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Problem 2:

In a basketball free-throw shooting contest, the shots made by Sam and Wil were in the ratio 7:9. Wil made 6 more shots than Sam. Find the number of shots made by each of them.

#### Step 1: Let variables represent shots
Let:
- Sam’s shots = $ 7x $
- Wil’s shots = $ 9x $

(We use $ x $ because the ratio is 7:9)

#### Step 2: Use the given difference
Wil made 6 more shots than Sam:
$$
9x - 7x = 6
$$
$$
2x = 6
$$
$$
x = 3
$$

#### Step 3: Find actual numbers
- Sam’s shots = $ 7x = 7 \times 3 = 21 $
- Wil’s shots = $ 9x = 9 \times 3 = 27 $

✔ Answer: Sam made 21 shots, and Wil made 27 shots.

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✔ Final Answers:

1) 275 boys
2) Sam: 21 shots, Wil: 27 shots