Question

The number of runners on a marathon team this year is 6 more than 4 times the number of runners on last year’s team. Half of the runners this year are female and half are male. What expression represents the number of female runners on the team this year? Does the expression (4r+6)/2 also represent the number of females on the team this year? Explain.

Answer 1

Let's use the variable r to represent the number of runners on last year's team and x to represent the number of runners this year.

Since the number of runners this year is 6 more than 4 times the number of runners on last year's team, we can write the following equation:

$x=4r+6$

Also, half the number of runners this year are females, so the expression for the number of females this year is:

$\text{females}=\frac{x}{2}=\frac{(4r+6)}{2}$

Therefore the answer is yes, the expression for the number of females is (4r+6)/2.