Question

of the model cars manufactured in September, 1/5 were models of race cars and 1/3 were world war ll vintage models.How many cars manufactured were neither race model cars nor world war ll vintage model cars

Answer 1

The fraction of cars that were race models, plus the fraction of cars that were world war ll vintage models, plus the fraction of cars that were neither race models nor world war ll vintage models, is equal to one.

Then, to find how many cars manufactured were neither race model cars nor world war ll vintage model cars we need to subtract 1/5 and 1/3 to 1, as follows:

$1-\frac{1}{5}-\frac{1}{3}=\frac{1\cdot5\cdot3-1\cdot3-1\cdot5}{5\cdot3}=\frac{15-3-5}{15}=\frac{7}{15}$

7/15 of the cars were neither race model cars nor world war ll vintage model cars.