SOLUTION: In a family there are two cars. The sum of the average miles per gallon obtained by the two cars in a particular week is 75 . The first car has consumed 25 gallons during that we

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Question 176336: In a family there are two cars. The sum of the average miles per gallon obtained by the two cars in a particular week is 75 . The first car has consumed 25 gallons during that week, and the second has consumed 35 gallons, for a total of 2275 miles driven by the two cars combined. What was the average gas mileage obtained by each of the two cars in that week?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
In a family there are two cars. The sum of the average miles per gallon obtained
by the two cars in a particular week is 75 . The first car has consumed 25
gallons during that week, and the second has consumed 35 gallons, for a total
of 2275 miles driven by the two cars combined. What was the average gas mileage
obtained by each of the two cars in that week?
:
Let x = av mi/gal of the 1st car
Let y = av mi/gal of the 2nd car
:
Total av mi/gal equation
x + y = 75
or
y = (75-x)
:
The total miles driven equation:
25x + 35y = 2275
:
Substitute (75-x) for y
25x + 35(75-x) = 2275
25x + 2625 - 35x = 2275
25x - 35x = 2275 - 2625
-10x = -350
x = +35 mpg for car 1
:
Find y:
:
y = 75 - x
y = 75 - 35
y = 40 mpg for car 2
;
;
check solution in total miles equation
25(35) + 35(40) = 2275
875 + 1400 = 2275