Answer :
The 1st car was consumed 40 gallons and the 2nd car was consumed 35 gallons
Step-by-step explanation:
A family has two cars
- The first car has a fuel efficiency of 25 miles per gallon of gas
- The second has a fuel efficiency of 30 miles per gallon of gas
- During one particular week, the two cars went a combined total of 2050 miles, for a total gas consumption of 75 gallons
We need to find how many gallons were consumed by each of the two cars that week
Assume that x represents the number of gallons was consumed by the 1st car and y represents the number of gallons was consumed by the 2nd care
∵ x represents the number of gallons was consumed by the 1st car
∵ y represents the number of gallons was consumed by the 2nd car
∵ The total gas consumption is 75 gallons
∴ x + y = 75 ⇒ (1)
∵ The 1st car has a fuel efficiency of 25 miles per gallon of gas
∵ The 2nd has a fuel efficiency of 30 miles per gallon of gas
∵ The two cars went a combined total of 2050 miles
∴ 25x + 30y = 2050 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by -30 to eliminate y
∵ -30x - 30y = -2250 ⇒ (2)
- Add equations (2) and (3)
∴ -5x = -200
- Divide both sides by -5
∴ x = 40
Substitute the value of x in equation (1) to find y
∵ 40 + y = 75
- Subtract 20 from both sides
∴ y = 35
The 1st car was consumed 40 gallons and the 2nd car was consumed 35 gallons
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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