Question

Car dealerships claim to make most of their money from servicing cars. In a certain month, an Acura dealership sold fifteen less used cars than twice the number of new cars. In the smae month, they serviced fifty more than twelve times the number of new cars sold. If the dealership either sold or services a total of 335 cars that month, how many new cars were sold that month? How many use? How many serviced?

Answer 1

New cars sold = 20,

Used cars sold = 25

Cars serviced = 290

Explanation:

In a month they sold fifteen less used cars than twice the number of new cars.

Lets say 'x' number of new cars were sold, then:

The number of used car sold is:

`2* x-15=2x-15`

In the same month they serviced fifty more than twelve times the number of new cars sold. So the number of cars serviced is:

`12* x+50=12x+50`

Altogether they sold or serviced 335 cars, so the sum of all the cars sold and serviced should be 335:

`x+(2x-15)+(12x+15)=335`

Solving for 'x' we get:

`x+2x+12x-15+50=335`

`15x+35=335`

`15x=335-35=300`

`x=(300)/(15)=20`

Therefore, the number of new cars sold in that month is 20.

Number of used car sold
`=2x-15=2* 20-15=40-15=25`

Number of cars serviced
`=12* x+50=12*20+50=240+50=290`

We can also cross check by summing them up:

`290+25+20=335`