second car gets an average of 40 miles per gallon. The two cars combined drive a total of 2050 miles in that week, for a total gas consumption of 70 gallons. How many gallons were consumed by each of the two cars that week?
2006-06-26 11:09:17 · 7 answers · asked by blackangelsp 1 in Science & Mathematics ➔ Mathematics
a = gallons used by car 1
b = gallons used by car 2
You can write two equations:
1) 15a + 40b = 2050
2) a + b = 70
Multiply #2 by 15 on both sides:
3) 15a + 15b = 1050
Subtract #3 from #1:
4) 25b = 1000
Solve for b:
5) b = 40
Solve for a (from #2)
6) a = 30
Double check your answers:
Car 1 goes 15 x 30 miles (450 miles)
Car 2 goes 40 x 40 miles (1600 miles)
Together they go 2050 miles
So the answer is:
First car 30 gallons
Second car 40 gallons
2006-06-26 11:16:29 · answer #1 · answered by Puzzling 7 · 2⤊ 0⤋
let x be the number of gallons used by the first car. The number of gallons used by the second car is 70 - x.
The distance driven by the first car is 15x
The distance driven by the second car is 40(70 - x)
The total distance driven is 2050 miles, so
15x + 40(70 - x) = 2050
15x + 2800 - 40x = 2050
-25x = -750
x = 30
So the first car consumed 30 gallons and the second consumed 40 gallons.
Check: 30 * 15 = 450 miles for the first car
40 * 40 = 1600 miles for the second car
Total of 2050 miles.
2006-06-26 11:17:20 · answer #2 · answered by mathsmart 4 · 0⤊ 0⤋
15(x) + 40(70-x) = 2050
15x + 2800 - 40x = 2050
25x = 750
x = 750/25 = 30.
15 (30) + 40 (30) = 2050
Car A consumed 30 Gallons and Car B consumed 40 Gallons.
2006-06-26 12:10:01 · answer #3 · answered by xmltrends 1 · 0⤊ 0⤋
CarA 15m/gal
CarB 40m/gal
CarA + CarB = 2050m
CarA/15gal + CarB/40gal = 70gal
You have two equations so solve solve for CarA and CarB.
A = 2050 - B
(2050 - B)/15 + B/40 = 70
B = 1600m
So...
A = 2050 - 1600 = 450m
So...
A = 450/15 = 30gal
B = 1600/40 = 40gal
2006-06-26 11:27:54 · answer #4 · answered by Haruki 1 · 0⤊ 0⤋
30 gallons in the 15 miles per gallon car....and 40 gallons in the 40 miles per gallon car. 450miles were driven in the 15 mile per gallon car, and 1600miles were driven in the 40 mile per gallon car...total miles driven=2050 miles... NEXT QUESTION PLEASE
2006-06-26 11:30:54 · answer #5 · answered by Anonymous · 0⤊ 0⤋
15x + 40y = 2050
x + y = 70
Multiply bottom by -15
15x + 40y = 2050
-15x - 15y = -1050
25y = 1000
y = 40
x + y = 70
x + 40 = 70
x = 30
30gal for the first care and 40gal for the second car.
2006-06-26 15:15:44 · answer #6 · answered by Sherman81 6 · 0⤊ 0⤋
40 mpg = 40 gal
15 mpg = 30 gal
2006-06-26 11:20:22 · answer #7 · answered by Tim D 4 · 0⤊ 0⤋