Question 1165931
miles divided by gallons = miles per gallon.


let x = the miles driven by the car that consumed 30 gallons of gas.


let y = the miles driven by the car that consumed 35 gallons of gax.


total miles driven is 1650.


your two equations are:


x + y = 1650
x/30 + y/35 = 50


the first equation tells you the total miles driven.
the second equation tells you the total miles per gallon consumed.


multiply both sides of the first eqution by 30 and multiply both sides of the second equation by 30 * 35 = 1050 to get:


30x + 30y = 49500
35x + 30y = 52500


subtract the first equation from the second to get:
5x = 3000


solve for x to get:
x = 600


since x + y = 1650, this makes y = 1050


you have x = 600 and y = 1050


check to see if these values make your original equations true.


your original equations are:
x + y = 1650
x/30 + y/35 = 50


these equations become:
600 + 1050 = 1650 which is true.
600/30 + 1050/35 = 50 which is also true.


miles / gallons = miles per gallon.


600/30 = 20 miles per gallon for the car that consumed 30 gallons.
1050/35 = 30 miles per gallon for the car that consumed 35 gallons.


those are your solutions.


to double check:


miles / miles per gallon = gallons consumed.


600/20 = 30 gallons
1050 / 30 = 35 gallons


it all checks out.


your solution is that the first car had a fuel efficiency of 20 miles per gallon and the second car has a fuel efficienty of 30 miles per gallon.