A car is twice as old as its radio was when the car was as old as the radio is. The sum of their ages is 49 years. How old is the car and how old is the radio?

Question

physics extra credit- please explain how to do the work

Answer 1

C is the present age of the car.

R is the present age of the radio.

Y marks a number of years ago.

C + R = 49

C = 2(R − Y)

C − Y = R

2R − 2Y = C

1R + 1Y = C

2R − 2Y = 49 − R

1R + 1Y = 49 − R

3R − 2Y = 49

2R + 1Y = 49

Simultaneous solution of the last pair of equations gives (R,Y) = (21,7).

Since C + R = 49, C is 28.

7 years ago, the car was (28 − 7) or 21 years old, which is the present age of the radio.

7 years ago, the radio was 14 years old, which means that the present age of the car (28)

is twice the age of the radio 7 years ago.