Problem solving using rational expressions

Question

A dealer bought some radios for a total of $1,400. She gave away 7 radios as gifts, sold the rest for $10 more than she paid for each radio, and broke even. How many radios did she buy?

Answer 1

Let R = number of radios
Let P = the price she paid for each radio

R*P = 1400 so P = 1400/R

and

(R-7)*(P+10) = 1400

substitute for P

(R - 7)*(1400/R + 10) = 1400

and multiply

1400 -(7)(1400)/R + 10R - 70 = 1400

multiply everything by R to get rid of the fraction

1400R -(7)(1400) + 10R^2 - 70R = 1400R

Combine like terms and reduce to get

R^2 - 7R - 980 = 0

Then factor to get

(R - 35)*(R + 28) = 0

So your solutions are 35 and -28.

Since you can't have a negative number of radios, the answer is 35 radios. Now you know that she paid $40/radio

You can check your solution. If she gave away 7, that leaves her with 28 radios. If she sold 28 radios for $50, she makes $1400.