Question

1. check for reasonableness the proportion $\frac{75}{w}=\frac{150}{100}$ can be used to find the whole, $w$. use the language of percent to explain whether $w$ is less than or greater than 75.

Explanation:

Step1: Analyze the proportion

The proportion $\frac{75}{w}=\frac{150}{100}$ means 75 is 150% of $w$. Since 150% is greater than 100%, 75 represents more than the whole ($w$) when considering percentages.

Step2: Determine the relationship

If 75 is 150% of $w$, then $w$ must be less than 75. We can also solve the proportion $\frac{75}{w}=\frac{150}{100}$ cross - multiply: $150w = 75\times100$, so $w=\frac{75\times100}{150}=50$.

Answer:

$w$ is less than 75.