SOLUTION: I don't understand how to set up this problem nor solve it? In a family there are two cars. In a given week,the first car gets an average of 25 miles per gallon, and the second

Question 155468: I don't understand how to set up this problem nor solve it?
In a family there are two cars. In a given week,the first car gets an average of 25 miles per gallon, and the second car gets 40 miles per gallon. The two cars combined drives a total of 1825 miles in that one week, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
In a family there are two cars. In a given week,the first car gets an average of 25 miles per gallon, and the second car gets 40 miles per gallon. The two cars combined drives a total of 1825 miles in that one week, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?
.
Let x = amt of gas consumed by first car
and y = amt of gas consumed by second car
.
25x + 40y = 1825 (equation 1)
x + y = 55 (equation 2)
.
solve equation 2 for y:
x+y = 55
y = 55-x
.
Use the above, and substitute it into equation 1 and solve for x:
25x + 40y = 1825
25x + 40(55-x) = 1825
25x + 2200 - 40x = 1825
2200 - 15x = 1825
- 15x = -375
x = -375/-15
x = 25 gallons (gas consumed by 25 mpg car)
.
From equation 2:
x + y = 55
25 + y = 55
y = 55-25
y = 30 gallons (gas consumed by 40 mpg car)
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