Practice test 5, Section 3, Prob 15: How would you think through this problem to get the right answer?

This is a tough one, right? The key is to come up with an equation for how much Alan spends on gas per week. You know he drives 100 miles, gets 25 miles per gallon of gas, and that gas costs $4 per gallon. From that info, we can say that:

\text{weekly gas cost}=\dfrac{100\text{ miles}}{25\text{ miles per gallon}}\times \$4\text{ per gallon}

Simplifying the right side will tell you that he spends $16 per week, but the structure of the equation is what’s important. Once you’ve got that, you can make the adjustment to figure out how many miles (m) he needs to drive to spend $5 (which of course is the same as the number of miles he needs to NOT drive to NOT spend $5):

\$5=\dfrac{m\text{ miles}}{25\text{ miles per gallon}}\times \$4\text{ per gallon}

Do a little rearranging and you’ve got answer choice D:

5=\dfrac{m}{25}\times 4

5=\dfrac{4}{25}m

\dfrac{4}{25}m=5