System of linear equations

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 25 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 60 gallons. How many gallons were consumed by each of the two cars?

Answer 1

1600 miles on 60 gallons

car A has 30 mpg

car B has 25 mpg

how far did each car go??

A+B = 60

30A + 25B = 1600

30A +25(60-A) = 1600

30A -25A = 1600 -25(60)

5A = 1600- 25(60)

A = 320 - 5(60) = 320-300 = 20 miles for car A

B = 60-20 = 40 miles for car B

check the answers

20(30)+40(25) = 600+1000 = 1600

Answer 2

Let x = the miles driven for first car

Let y = the miles driven for the second car

x+y = 1600 Equation 1

x/30 + y/25 = 60

Finding common denominator

(25x + 30y)/750 = 60 --> 25x + 30y = 60(75) = 4500 Equation 2

Subtract 25 times the first equation from the second equation to eliminate x.

25x + 30y = 45000

-25x - 25y = -40000

--------------------------

0x + 5y = 5000

y = 5000/5 = 1000

x = 1600 -y = 600

x/30 = 600/30 = 20 gallons for the first car

y/25 = 1000/25 = 40 gallons for the second car

Answer 3

Car 1 30 mpg or m₁ = 30g₁

Car 2 25 mpg or m₂ = 25g₂

m₁ + m₂ = 1600 miles

g₁ + g₂ = 60 gals g₁ = 60 - g₂ Use replacement method.

30g₁ + 25g₂ = 1600 → 30(60 - g₂) + 25g₂ = 1600

1800 - 30g₂ + 25g₂ = 1600 → 200 = 5g₂ ; g₂ = 40 gal; so g₁ = 20 gal

Check: Car₁ = 20 gal x 30 mpg = 600 mi

Car₂ = 40 gal x 25 mpg = 1000 mi. Total 1600 mi.

Answer 4

f represents the gallons of the first car

60 - f represents the gallons of the second car

30f + 20(60 - f) = 1600

Can you solve for f and answer?