Question

choose tools use a model to answer the question. use a proportion to check your answer. 48 is 75% of what number? 48 is 75% of \square.

Explanation:

Step1: Define the variable

Let \( x \) be the number we are looking for. We know that \( 75\% \) of \( x \) is 48. Mathematically, this can be written as \( 0.75x = 48 \) (since \( 75\% = 0.75 \)).

Step2: Solve for \( x \)

To find \( x \), we divide both sides of the equation by \( 0.75 \):
\( x=\frac{48}{0.75} \)
Calculating the right - hand side, \( \frac{48}{0.75}=64 \).

Step3: Check using proportion

We know that the proportion for percentage problems is \( \frac{\text{part}}{\text{whole}}=\frac{\text{percentage}}{100} \). Here, the part is 48, the percentage is 75, and the whole is \( x \). So we set up the proportion \( \frac{48}{x}=\frac{75}{100} \).
Cross - multiply: \( 75x = 48\times100 \)
\( 75x=4800 \)
Divide both sides by 75: \( x=\frac{4800}{75}=64 \)

Answer:

64