Question

Elmer's new car gets $50\%$ better fuel efficiency, measured in kilometers per liter, than his old car. However, his new car uses diesel fuel, which is $20\%$ more expensive per liter than the gasoline his old car uses. By what percent will Elmer save money if he uses his new car instead of his old car for a long trip?

$20\%$

$26\tfrac23\%$

$27\tfrac79\%$

$33\tfrac13\%$

$66\tfrac23\%$

Solution:

Every liter can get $1.5$ times as many kilometers per liter. This is the same thing as saying he needs $\frac 23$ as many liters as per kilometer. However, each liter will cost $1.2$ times as many dollars as before.

We need to find the change in dollars over kilometer for the change in cost for the trip. We can see that the change is $1.2$ dollars per liter times $\frac 23$ liters per kilometer. Solving this, we have $1.2\cdot \frac 23 =\frac 45$ of the cost.

He therefore saves $\frac 15$ of the total cost. As such, the savings is $20 \%.$

Thus, the correct answer is A .

2017 AMC 10B Problem 12

Solution:

Problem 12 in Other Years