Question 1188880
A family has two cars. 
During one particular week, the first car consumed 30 gallons of gas and the second consumed 35 gallons of gas.
 The two cars drove a combined total of 2425 miles, and the sum of their fuel efficiencies was 75 miles per gallon.
 :
let a = distance traveled by car 1
let b = distance traveled by car 2
:
Two equations, arrange for elimination 
{{{a/30}}} + {{{b/35}}} = 75
multiply by the LCD, 210, cancel the denominators
7a + 6b = 210 * 75
7a + 6b = 15750
and 
a + b = 2425
multiply by 6
6a + 6b = 14550
:
7a + 6b = 15750
6a + 6b = 14550
-------------------Subtraction eliminates b, find
a = 1200 mi driven by the 1st car
then
2425 - 1200 = 1225 mi driven by the 2nd car
:
"What were the fuel efficiencies of each of the cars that week?"
1200/30 = 40 mpg for the 1st car
and
1225/35 = 35 mpg for the 2nd car