Help, help me, I'm losing my sanity.

Question

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1,550. What was the rate charged per hour by each mechanic if the sum of the two rates was $195 per hour?

Answer 1

x+y = 195

multiply by 10

10x+10y= 1950 subtract

10x + 5y = 1550 to eliminate one variable and get

5y = 400

y = $80 per hour for 2nd mechanic's rate

x = 195-80 = $115 per hour for 1st mechanic's rate