Question

A family has two cars. The first car has a fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas. During one week, the two cars went a combined total of 1700 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

Answer: The number of gallons consumed by first car and second car are 30 gallons and 20 gallons respectively.

Explanation:

Let the number of gallons used by the first car be 'x'.

Let the number of gallons used by the second car be 'y'.

Fuel efficiency of first car = 30 miles per gallon

Fuel efficiency of second car = 40 miles per gallon

So, According to question, it becomes,

`x+y=50------------(1)\\30x+40y=1700-----------(2)`

From eq(1), we get x= 50-y.

Put the above value in eq(2), we get that

`30(50-y)+40y=1700\\\\1500-30y+40y=1700\\\\10y=1700-1500\\\\10y=200\\\\y=(200)/(10)\\\\y=20`

x=50-20=30 gallons

Hence, the number of gallons consumed by first car and second car are 30 gallons and 20 gallons respectively.

Answer 2

The number of gallons consumed by the first car were 30

The number of gallons consumed by the second car were 20

Explanation:

Let

x -----> number of gallons consumed by the first car during one week

y -----> number of gallons consumed by the second car during one week

we know that

The efficiency multiplied by the number of gallons is equal to miles

30x+40y=1,700 -----> equation A

x+y=50 ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (30,20)

see the attached figure

therefore

The number of gallons consumed by the first car were 30

The number of gallons consumed by the second car were 20