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.
Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!
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 =  , or  miles per gallon
S = 45 25 ------- Substituting 25 for F in eq (i)
S, or fuel efficiency for car 2 =  miles per gallon
You can do the check!!
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