Question

solve ratio problems whith proportions

Answer 1

Sure! Solving ratio problems using proportions involves setting up a relationship between two ratios and then solving for an unknown value. Here’s the step-by-step method for solving such problems:

### Steps to Solve Ratio Problems Using Proportions

1. **Identify the Ratios**: Determine the two ratios that are given in the problem.

2. **Set Up a Proportion**: Write the two ratios as a fraction and set them equal to each other.

3. **Cross Multiply**: This step involves multiplying across the equals sign to create an equation.

4. **Solve for the Unknown**: Isolate the variable and solve for it.

### Example Problem 1

**Problem**: If 3 apples cost $1.50, how much do 5 apples cost?

**Step 1**: Identify the Ratios
- Ratio of apples to cost: \( 3 \text{ apples} : 1.50 \text{ dollars} \)

**Step 2**: Set Up the Proportion
Let \( x \) be the cost of 5 apples.
\[
\frac{3 \text{ apples}}{1.50 \text{ dollars}} = \frac{5 \text{ apples}}{x \text{ dollars}}
\]

**Step 3**: Cross Multiply
\[
3x = 1.50 \times 5
\]
\[
3x = 7.50
\]

**Step 4**: Solve for the Unknown
\[
x = \frac{7.50}{3} = 2.50
\]
Thus, 5 apples cost $2.50.

### Example Problem 2

**Problem**: A recipe requires a ratio of 2 cups of flour to 3 cups of sugar. If you want to use 4 cups of flour, how much sugar do you need?

**Step 1**: Identify the Ratios
- Ratio of flour to sugar: \( 2 \text{ cups flour} : 3 \text{ cups sugar} \)

**Step 2**: Set Up the Proportion
Let \( y \) be the amount of sugar needed when using 4 cups of flour.
\[
\frac{2 \text{ cups flour}}{3 \text{ cups sugar}} = \frac{4 \text{ cups flour}}{y \text{ cups sugar}}
\]

**Step 3**: Cross Multiply
\[
2y = 3 \times 4
\]
\[
2y = 12
\]

**Step 4**: Solve for the Unknown
\[
y = \frac{12}{2} = 6
\]
Thus, you need 6 cups of sugar when using 4 cups of flour.

### Summary
- Identify ratios and set up a proportion.
- Cross multiply to form an equation.
- Solve for the unknown variable.

If you have a specific problem in mind, feel free to share it, and I can help you solve it!