# A couple travels 420 miles to drop their daughter off at summer camp. The trip back has a short cut and is only 360 miles, and the gas mileage is 50% better due to a lighter load. How do you write an equation for the total gas used, and simplify?

Call the gas used on the way to camp '$g$'.
Then the fuel used on the way back will be $\frac{360}{420} \times 0.5 \times g$.
We need to add this to the '$g$' used on the way, so we get...
Total fuel used: $g + \frac{360}{420} \times 0.5 \times g = g + 0.43 g = 1.43$ $g$