Question

high school math ratio problems

Answer 1

Sure! Here are some high school math ratio problems along with their solutions:

### Problem 1: Ratio of Ages
Sophia is 12 years old and her brother, Ethan, is 8 years old. What is the ratio of their ages, and what will the ratio be in 5 years?

**Solution:**
Current age ratio of Sophia to Ethan:
\[
\text{Ratio} = \frac{Sophia's \, age}{Ethan's \, age} = \frac{12}{8} = \frac{3}{2}
\]

In 5 years, Sophia will be 17 and Ethan will be 13:
\[
\text{New Ratio} = \frac{17}{13}
\]

### Problem 2: Mixing Paint
A painter mixes red and blue paint in the ratio of 4:3. If the painter wants to make 21 liters of paint, how many liters of red and blue paint should he use?

**Solution:**
Let the amount of red paint be \( 4x \) and blue paint be \( 3x \). So,
\[
4x + 3x = 21
\]
\[
7x = 21 \quad \Rightarrow \quad x = 3
\]
Then,
- Red paint: \( 4x = 4 \times 3 = 12 \) liters
- Blue paint: \( 3x = 3 \times 3 = 9 \) liters

### Problem 3: Ratio of Distances
A car travels 120 miles in 2 hours while a bike travels 30 miles in 1 hour. What is the ratio of the distance traveled by the car to the bike?

**Solution:**
Car's distance = 120 miles
Bike's distance = 30 miles
Ratio of distances:
\[
\text{Ratio} = \frac{120}{30} = 4:1
\]

### Problem 4: Sharing Money
Alice and Bob have a combined total of $180. If Alice has three times as much money as Bob, how much money does each person have?

**Solution:**
Let Bob's amount be \( x \). Then Alice's amount is \( 3x \).
\[
x + 3x = 180
\]
\[
4x = 180 \quad \Rightarrow \quad x = 45
\]
So, Bob has $45, and Alice has:
\[
3x = 3 \times 45 = 135
\]

### Problem 5: Ratio of Speeds
Two runners are racing. Runner A runs at a speed of 10 km/h while Runner B runs at a speed of 15 km/h. What is the ratio of their speeds?

**Solution:**
Ratio of speeds:
\[
\text{Ratio} = \frac{10}{15} = \frac{2}{3}
\]

### Problem 6: Recipe Adjustment
A recipe calls for 2 cups of sugar for every 3 cups of flour. If you want to use 9 cups of flour, how many cups of sugar do you need?

**Solution:**
The ratio of sugar to flour is \( \frac{2}{3} \).
Let the cups of sugar be \( x \):
\[
\frac{x}{9} = \frac{2}{3}
\]
Cross-multiplying gives:
\[
3x = 18 \quad \Rightarrow \quad x = 6
\]
You need 6 cups of sugar.

Feel free to ask for more problems or explanations on a specific topic!