Question

Question 9

Answer 1

The first car consumed 40 gallons of gas and second car consumed 30 gallons of gas

Solution:

Let x = gallons consumed by car 1

Let y = gallons consumed by car 2

Fuel efficiency of car 1 = 15 miles per gallon

Distance covered in 1 gallon of gas = 15 miles

Fuel efficiency of car 2 = 25 miles per gallon

Distance covered in 1 gallon of gas = 25 miles

Given a total gas consumption of 70 gallons

Therefore,

gallons consumed by car 1  + gallons consumed by car 2 = 70

x + y = 70 ------ eqn 1

The two cars went a combined total of 1350 miles

Therefore,

gallons consumed by car 1  x distance covered in 1 gallon of gas of car 1 + gallons consumed by car 2 x distance covered in 1 gallon of gas of car 2 = 1350

$x \times 15 + y \times 25 = 1350$

15x + 25y = 1350 ----- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 70 - y ------- eqn 3

Substitute eqn 3 in eqn 2

15(70 - y) + 25y = 1350

1050 - 15y + 25y = 1350

10y = 1350 - 1050

10y = 300

y = 30

Substitute y = 30 in eqn 3

x = 70 - 30

x = 40

Thus first car consumed 40 gallons of gas and second car consumed 30 gallons of gas