Question

recent scott and michele were house - shopping. in one neighborhood, they noticed that 24% of the houses for sale were above their budget. if there were 50 houses for sale, how many were above their budget? determine if the statements are true or false. select the correct answer in each row. statement 24 houses are above their budget. the proportion $\frac{x}{100}=\frac{24}{50}$ can be used to solve. 48 houses are above their budget. the proportion $\frac{x}{100}=\frac{24}{50}$ can be used to solve. 12 houses are above their budget. true false

Explanation:

Step1: Recall proportion formula

The proportion formula for finding a percentage is $\frac{\text{part}}{\text{total}}=\frac{\text{percentage}}{100}$. Here, the total number of houses is 50 and the percentage of houses above - budget is 24. Let the number of houses above - budget be $x$. So the correct proportion is $\frac{x}{50}=\frac{24}{100}$.

Step2: Analyze each statement

• For the statement "24 houses are above their budget": We need to solve the proportion $\frac{x}{50}=\frac{24}{100}$ to find $x$. Cross - multiplying gives $100x = 24\times50$, so $x = 12$. So this statement is False.
• For the statement "The proportion $\frac{24}{50}=\frac{x}{100}$ can be used to solve": The correct proportion should have the part over the total on one side and the percentage over 100 on the other. The correct one is $\frac{x}{50}=\frac{24}{100}$, not $\frac{24}{50}=\frac{x}{100}$. So this statement is False.
• For the statement "48 houses are above their budget": Since solving $\frac{x}{50}=\frac{24}{100}$ gives $x = 12$, this statement is False.
• For the statement "The proportion $\frac{x}{50}=\frac{24}{100}$ can be used to solve": This is the correct proportion for finding the number of houses above budget given the total number of houses (50) and the percentage (24%), so this statement is True.
• For the statement "12 houses are above their budget": Solving the proportion $\frac{x}{50}=\frac{24}{100}$: Cross - multiply: $100x=24\times50$, $100x = 1200$, $x = 12$. So this statement is True.

Answer:

Statement	True/False
The proportion $\frac{24}{50}=\frac{x}{100}$ can be used to solve.	False
48 houses are above their budget.	False
The proportion $\frac{x}{50}=\frac{24}{100}$ can be used to solve.	True
24 houses are above their budget.	False