Question

Transit Department of one town has collected information about its vehicles. There are three times as many public vehicles as private vehicles. 20 percent of the public vehicles are powered by alternative fuels, of which 40 percent are powered by bio fuels, 20 percent by hydrogen, and the remainder by natural gas. 25 percent of private vehicles are less than 5 years old, which is half the rate for natural gas public vehicles. Select the option that indicates percentage of town vehicles are natural gas public vehicles that are at least 5 years old ?

Answer 1

Answer:

47.92%

Step-by-step explanation:

Let x denote the number of private vehicles.

If there are three times as many public vehicles as private vehicles,

Then, the number of public vehicles is

$3*x= 3x$

The number of public vehicles that are powered by alternative fuels is

$3x*0.2=0.6x$

The number of public vehicles that are powered by bio fuels is

$0.6x*0.4=0.24x$

The number of public vehicles that are powered by hydrogen is

$0.6x*0.2=0.12x$

The number of public vehicles that are powered by natural gas is

$0.6x*0.4=0.24x$

The number of private vehicles that are less than 5 years old is

$x*0.25=0.25x$

0.25x is equivalent to half the number of public vehicles powered by natural gas that are less than 5 years

Therefore the number of public vehicles powered by natural gas that are less than 5 years is 0.125x

Therefore the number of public vehicles powered by natural gas that are at least 5 years is

$0.24x-0.125x=0.115x$

percentage of town vehicles are natural gas public vehicles that are at least 5 years old  is

$\frac{0.115x}{0.24x}*100=47.92%$