A certain car can currently travel 20 miles per gallon of gasoline. After a tune-up, the car will use 80 percent as much gasoline as it does now. How many miles will the car be able to travel per gallon of gasoline after the tune-up?
A. 15 B. 16 C. 24 D. 25 E. 28
(D) After the tune-up, the car will travel 20 miles on 80% of a gallon of gasoline, which means it will travel 20 miles on 8/10, or 4/5, of a gallon of gasoline.
To solve for the number of miles that the car will be able to travel per one gallon of gasoline, we need to set up the following proportion: 20 miles is to 4/5 gallon as X miles is to 1 gallon.
Algebraically, this is expressed as: 20/(4/5) = X/1 X = 20 × 4/5 X = 25
So the car will be able to travel 25 miles per gallon of gasoline after the tune-up. The correct answer is choice (D). -----------
In this question you state that the car will use 80% AS MUCH GASOLINE AS IT DOES NOW. According to my understanding this should be - what the car uses now plus 80% not 80% of the current usage. Am I right? Or could you please explain the wording of the question? Thank you.
This question is quite confusing. When you say the car will use 80% as much gasoline as it does now, this should mean 80% more of its current use not 80% of its current use, shouldn't it?
Note, that "80% of the value" is "0.8 × value". Consider similar phrases with integer multipliers: "Canada job creation is four times as much as forecast" means CREATED JOBS = 4 × PREDICTED VALUE, NOT "CREATED JOBS = 5 × PREDICTED VALUE"
"People value the Internet 13 times as much as a nice meal out" means people value the Internet = 13 × people value a nice meal out, NOT "people value the Internet = (13 + 1) × people value a nice meal out"
The same is in the question statement phrase: "After a tune-up, the car will use 80 percent as much gasoline as it does now." means the car will use 0.8 times as much gasoline as it does now. new consumption = 0.8 × current consumption, NOT "new consumption = (1 + 0.8) × current consumption."
But the simplest way to calculate this is 20/0.8 and the answer will be 25.
That's exactly what we did, X = 20 / (4/5). The given solution is a very detailed one and gives us the explanation of why this formula works here. If you are familiar with the reasoning and feel comfortable of applying it right away, go ahead. (Especially, if you practiced questions of such type).
However if you don't feel confident, or want to take extra precautions and have spare time redoing this reasoning will increase chance of avoiding a mistake.
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