Question 783856

A family has two cars. During one particular week, the first car consumed 30 gallons of gas and the second consumed 35 gallons of gas. The two cars drove a combined total of 1450 miles, and the sum of their fuel efficiencies was 45  miles per gallon. What were the fuel efficiencies of each of the cars that week?

I am having trouble setting this up. Could you please help me?
Thank you.


Let fuel efficiency for car 1 and car 2 be F, and S, respectively
Then F + S = 45 ------- S = 45 – F ------ eq (i)
Also, 30F + 35S = 1,450 ------ eq (ii)
30F + 35(45 – F) = 1,450 ---------- Substituting 45 – F for S in eq (ii)
30F + 1,575 – 35F = 1,450
30F - 35F = 1,450 – 1,575 
– 5F = - 125


F, or fuel efficency for car 1 = {{{(- 125)/- 5}}}, or {{{highlight_green(25)}}} miles per gallon


S = 45 – 25 ------- Substituting 25 for F in eq (i)
S, or fuel efficiency for car 2 = {{{highlight_green(20)}}} miles per gallon


You can do the check!! 


Further help is available, online or in-person, for a fee, obviously. Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com