Question

the owner of a go-kart racetrack would like to have a ratio of 2 red racers for every 3 green mini-trucks. the racetrack currently has 11 red racers and 21 mini-trucks. which equation could she use to determine x, the number of additional red racers she should purchase in order to achieve the desired ratio?
a) $\frac{11+x}{21-x}=\frac{2}{3}$
b) $\frac{11+x}{21}=\frac{2}{3}$
c) $\frac{11-x}{21}=\frac{2}{3}$
d) $\frac{11+x}{21+x}=\frac{2}{3}$

Explanation:

Step1: Define final red racer count

The current number of red racers is 11, and we add \(x\) more, so the final count is \(11 + x\).

Step2: Identify green truck count

The number of green mini-trucks stays 21 (no change mentioned).

Step3: Set up desired ratio

The desired ratio of red racers to green trucks is \(\frac{2}{3}\), so equate the final counts to this ratio:
$\frac{11+x}{21} = \frac{2}{3}$

Answer:

B. $\frac{11+x}{21}=\frac{2}{3}$