Question

There are r racecars in the toy box but four are broken. Terrance and Cynthia share the working racecars in a ratio of 1:3. Which expression represents the number of racecars Cynthia plays with?

A) (4r - 4) racecars
B) racecars
C) (3r - 12) racecars
D) (r - 3) racecars

Answer 1

Cynthia plays with three-fourths of the working racecars after r - 4 are accounted for broken ones. The expression representing her share is (3r - 12) racecars.

Step-by-step explanation:

The expression that represents the number of racecars Cynthia plays with is found by first accounting for the broken racecars and then distributing the remaining ones according to the given ratio. Since four racecars are broken, we need to subtract 4 from the total number r to get the number of working racecars, which is r - 4. Terrance and Cynthia share these remaining racecars in a 1:3 ratio, meaning for every 1 racecar Terrance plays with, Cynthia plays with 3. To find out how many racecars Cynthia plays with, we should first determine the total parts in the ratio, which is 1 + 3 = 4 parts. Then, we distribute the working racecars (r - 4) into these 4 parts and multiply it by 3 parts to get Cynthia's share, which gives us (3/4) × (r - 4). This simplifies further to (3r - 12) racecars, indicating that Cynthia plays with three-fourths of the working racecars.