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Question 1188880: 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 2425 miles, and the sum of their fuel efficiencies was 75 miles per gallon. What were the fuel efficiencies of each of the cars that week?
Found 3 solutions by josgarithmetic, ankor@dixie-net.com, greenestamps:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website!
FUEL EFFIC. RATE VOLUME DISTANCE
firstcar 75-r 30 30(75-r)
secondcar r 35 35r
TOTAL 75 2425
Maybe you can decide what to do next from this.
Answer by ankor@dixie-net.com(22740)  (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 2425 miles, and the sum of their fuel efficiencies was 75 miles per gallon.
:
let a = distance traveled by car 1
let b = distance traveled by car 2
:
Two equations, arrange for elimination
 +  = 75
multiply by the LCD, 210, cancel the denominators
7a + 6b = 210 * 75
7a + 6b = 15750
and
a + b = 2425
multiply by 6
6a + 6b = 14550
:
7a + 6b = 15750
6a + 6b = 14550
-------------------Subtraction eliminates b, find
a = 1200 mi driven by the 1st car
then
2425 - 1200 = 1225 mi driven by the 2nd car
:
"What were the fuel efficiencies of each of the cars that week?"
1200/30 = 40 mpg for the 1st car
and
1225/35 = 35 mpg for the 2nd car
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
I personally think this is more easily solved using two variables....
let x = mpg for first car
let y = mpg for second car
Then
x+y=75 the combined fuel efficiency ( a strange measurement...!) is 75mpg
30x+35y=2425 the total miles was 2425
Multiply the first equation by 30 and solve by elimination:
30x+30y=2250
30x+35y=2425
5y=175
y=35
x=40
ANSWERS: 40mpg for the first car; 35 for the second
CHECK: 40(30)+35(35)=1200+1225=2425
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