Answer:
[tex]\huge\boxed{\text{First Car: 25 gallons}}[/tex]
[tex]\huge\boxed{\text{Second Car: 15 gallons}}[/tex]
Step-by-step explanation:
In order to find how many gallons of fuel were used by each car, we need to understand what everything means.
If you travel 15 miles per gallon, then every 15 miles travelled will be 1 gallons of fuel used. Same logic applies for 40 miles per gallon.
We can assign each car's total gallons used to variables - let's call the first car x and the second car y.
To find the distance that each car travelled, we can make an expression for each.
First car: [tex]15x[/tex], since you go 15 miles per gallon.
Second car: [tex]40y[/tex] since you go 40 miles per gallon.
Since these cars combined went a total of 975 miles, we can make an equation.
[tex]15x+40y=975[/tex]
We also know the total fuel consumption was 40 gallons. Therefore:
[tex]x+y=40[/tex]
We can now solve this systems of equations. Let's use the elimination method, where we manipulate one expression so we can get rid of a variable.
- [tex]15x+40y=975\\x+y=40[/tex]
- [tex]-15(x+y =40)[/tex]
- [tex]-15x-15y=-600[/tex]
- [tex]15x+40y=975\\-15x-15y= -600[/tex]
- [tex]25y=375[/tex] (15x and -15x cancel out)
- [tex]y=15[/tex]
So we know the second car consumed 15 gallons of fuel. We can now substitute this back into [tex]x+y=40[/tex] as y to find the value of x.
- [tex]x+15=40[/tex]
- [tex]x=40-15[/tex]
- [tex]x=25[/tex]
So the first car consumed 25 gallons and the second car consumed 15.
Hope this helped!
