Respuesta :
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
[tex]x \times 15 + y \times 25 = 1350[/tex]
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
