Quantitative Literacy Practice Exam

In a county with 6,272 homes, if homes without children outnumber those with children in a ratio of 9:7, how many homes are without children?

1. 3,528

2. 3,800

3. 2,840

4. 4,000

The correct answer is: 3,528

To determine the number of homes without children based on the provided ratio and total number of homes, we start by interpreting the ratio of homes without children to those with children, which is given as 9:7. This means for every 9 homes without children, there are 7 homes with children. First, we need to express the total number of homes in terms of this ratio. The combined parts of the ratio (9 parts without children and 7 parts with children) equal 16 parts (9 + 7 = 16). Next, let’s do the following calculations: 1. Calculate the value of one part by dividing the total number of homes (6,272) by the total number of parts (16): \[ \text{Value of one part} = \frac{6,272}{16} = 392 \] 2. Now, to find the number of homes without children, we multiply the number of parts representing homes without children (9) by the value of one part: \[ \text{Homes without children} = 9 \times 392 = 3,528 \] Thus, the number of homes without children is 3,528