Question

PLEASE HELP!!!!!!! A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 1450 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

The answer to your question is car 1 = 30 gal and car 1 = 20 gal

Explanation:

car 1 = a

car 2 = b

Efficiency of car 1 = 35 mi/gal

Efficiency for car 2 = 20 mi/gal

Total distance = 1450

Total gas consumption = 50 gal

Equations

35a + 20b = 1450 ------- (I)

a + b = 50 ------- (II)

Solve by elimination

Multiply equation II by -35

35a + 20b = 1450

-35a - 35b = -1750

Simplify

0 - 15b = -300

Solve for b

b = -300/-15

Result

b = 20

Substitute b in equation II to find a

a + 20 = 50

Solve for a

a = 50 -20

Result

a = 30