SOLUTION: A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular w
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Question 1149259: A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1600 miles, for a total gas consumption of 65 gallons. How many gallons were consumed by each of the two cars that week? Answer by ikleyn(52786) (Show Source):
Let x = the number of gallons consumed by the 1-st car and y = that for the 2-nd car.
Then you have this system of 2 equations in 2 unknowns
x + y = 65 (1) (65 gallons of gas, total)
40x + 15y = 1600 (2) (miles, total)
There are many methods to solve the system.
For example, you may use the Elimination method.
For it, multiply eq(1) by 40 (both sides). Keep eq(2) as is
40x + 40y = 65*40 (1')
40x + 15y = 1600 (2')
Next, subtract eq(2') from eq(1). You will get
40y - 15y = 65*40 - 1600
25y = 1000
y = 1000/25 = 40.
ANSWER. 2-nd car consumed 40 gallons of gas; 1-st car consumed the rest 65-40 = 25 gallons.
