Solving a value mixture problem using linear equations

Question

A family has two cars. During one week, the first car consumed 25 gallons of gas and the second consumed 15 gallons of gas. The two cars drove a combined total of 1375 miles, and the sum of their fuel efficiency was 65 miles per gallon. What was the fuel efficiencies of each of the cars that week

Answer 1

1375 = total miles driven on 25+15 = 40 gallons of gas

1375/40 = 34.375 = 34 3/8 mpg average

x + y = 65

(x)25 + 15y = 1375

15x + 15y = 15(65) = 975

subtract to get

10x = 400

x = 40 mpg, = 1st car's mpg

y = 25 mph = 2nd car's mpg

40 mpg x25 gal = 1000 miles for 1st car

25 mpg x15 gal = 225 miles for 2nd car

1000+375 = 1375 miles It works

40 - 34 3/8 = 5 5/8

34 3/8 - 25 = 9 3/8

9 3/8 over 5 5/8 = 75/45 = 15/9 = 5/3

5/3 = f/s = (65-s)/s

cross multiply

5s = 195 -3s

8s = 195'

s = 24 3/8 mpg for 2nd car

65 -s = 40 1/8 mph for 1st car'

40 1/8 mpg x 25 gal = 1000 25/8 miles

24 3/8 x 15 gal = 360 45/8 miles

sum = 1360 70/8 = 1368 1/2 miles which is close to 1375 but off by 7 miles

go with 40 and 25 mpg and 1st method of solving this problem

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