Question

Solve ratio problems with proportions quick check

Answer 1

Sure! Here’s a quick guide to solve ratio problems using proportions.

### Steps to Solve Ratio Problems:

1. **Understand the Ratios**: Ratios show the relationship between two quantities. For example, if the ratio of A to B is 3:4, it means for every 3 of A, there are 4 of B.

2. **Set up the Proportion**: When given a ratio problem, you can set it up as a proportion. If you know one quantity and its corresponding ratio, you can find the unknown.

For example, if the ratio of A to B is 3:4 and you know A = x, you can set up the proportion:
\[
\frac{A}{B} = \frac{3}{4} \implies \frac{x}{B} = \frac{3}{4}
\]

3. **Cross-Multiply**: Once you have the proportion:
\[
x \times 4 = 3 \times B \implies 4x = 3B
\]

4. **Solve for the Unknown**: Rearrange the equation to find the unknown quantity. If looking for B, you would solve:
\[
B = \frac{4x}{3}
\]

### Example Problem:

**Problem**: The ratio of apples to oranges is 2:5. If there are 10 apples, how many oranges are there?

**Solution**:

1. Set up the ratio: \(\frac{A}{O} = \frac{2}{5}\) where \(A\) is apples and \(O\) is oranges.
2. Plug in the known value:
\[
\frac{10}{O} = \frac{2}{5}
\]
3. Cross-multiply:
\[
10 \times 5 = 2 \times O \implies 50 = 2O
\]
4. Solve for \(O\):
\[
O = \frac{50}{2} = 25
\]

**Answer**: There are 25 oranges.

### Practice Quick Check:

1. The ratio of boys to girls in a class is 3:2. If there are 15 boys, how many girls are there?
2. A recipe uses sugar and flour in a ratio of 1:4. If you have 2 cups of sugar, how much flour do you need?
3. The ratio of cats to dogs is 5:3. If there are 12 cats, how many dogs are there?

Feel free to solve them, and if you'd like, I can check your answers!