Question

How can you use equivalent ratios to find the whole given the part and the percent?

Answer 1

To find the whole given a part and a percentage using equivalent ratios, you can set up the problem as a proportion. Let's break it down step by step:

1. **Understand the Ratio**: If you have a part (let's call it \( P \)) and a percentage (let's call it \( r\% \)), this percentage represents the part of the whole. The relationship can be expressed as:
\[
\frac{P}{\text{Whole}} = \frac{r}{100}
\]

2. **Set Up the Equation**: Rearrange the equation to find the whole. If you want to express this in a formula, you can multiply both sides by the whole to isolate it:
\[
P = \frac{r}{100} \times \text{Whole}
\]

To find the Whole, rearranging gives:
\[
\text{Whole} = \frac{P \times 100}{r}
\]

3. **Calculate the Whole**: Now, you can plug in your values for \( P \) and \( r \) into this formula to calculate the whole.

### Example:
Imagine you have a part of 30 and you know that this part represents 25% of the whole.

1. Identify your values:
- \( P = 30 \)
- \( r = 25 \)

2. Plug these into the formula:
\[
\text{Whole} = \frac{30 \times 100}{25}
\]

3. Perform the calculation:
\[
\text{Whole} = \frac{3000}{25} = 120
\]

So, in this example, the whole is 120.

Using equivalent ratios in this way allows you to solve for the unknown whole when you have a part and the percentage it represents.