How many cars were used? (re)

Question

A car dealership makes $191,000, used cars were sold for $7000 and new cars were sold for $16,000, a total of 17 cars were sold.

 

How many used cars were sold?

 

So this is how I tried to solve it:

 

x = 7

y = 16

17 - y = x

 

7x + 16y = 191

7(17-y) + 16y = 191

119 - 191 = 72

7 = 72

y = 10.2 (?) (I divided 72 by 7 here and got 10.2)

10.2 - 17 = 6.8

x = 6.8

 

used cars = 6.8 (??)

 

Obviously im doing something wrong here, can someone please help?

 

 

(By the way i reposted this question because the commenting system wasn't working properly in my previous post.)

 

 

 

 

EDIT: Well I can't comment and reply back to you Andrew so this is my only way of communication. I want to say thank you very much, I understand it now. Thank you very much for your insight and help!

Answer 1

Let u = number sold used cars

Let n = number sold new cars

 

u + n = 17

7000u + 16000n = 191000

Let's reduce this by factoring out 1000

7u + 16n = 191

 

From 1st equation; u = 17-n

Substitute into 2nd equation:

7(17-n) + 16n = 191

119 - 7n + 16n = 191

119 + 9n = 191

9n = 72

n = 8     There were 8 new cars sold

u = 17-n = 9 used cars sold

 

Check:  9(7000) + 8(16000) = 63000 + 128000 = $191,000

 

Understand?