Preparing for ASVAB: Given 3.79L/gal, $3.36/gal, find cost of 1 L.

Madgod483

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Hey everyone,

I'm having a problem understanding this Arithmetic problem, and while it explained it to me in detail how it got the answer. I'm still having trouble and am asking for someone to break it down for me some more. Thanks in advance!!


12.If there are 3.79 liters in a gallon, and gasoline costs $3.36 per gallon, how much does a liter of gas cost to the nearest cent?
A) $0.88
B) $0.89
C) $1.12
D) $1.13



StatusCorrectExplanation
correct.gif
Correct
BSince there are two known ratios (gallons per 3.79 liters and dollars per gallon), multiply them together so gallons will cancel out, and you will be left with the cost per liter. (1 gallon)/(3.79 liters) x $3.36/(1 gallon) = 0.887, so choice (B) is the correct answer.
 
Hey everyone,

I'm having a problem understanding this Arithmetic problem, and while it explained it to me in detail how it got the answer. I'm still having trouble and am asking for someone to break it down for me some more. Thanks in advance!!


12.If there are 3.79 liters in a gallon, and gasoline costs $3.36 per gallon, how much does a liter of gas cost to the nearest cent?
A) $0.88
B) $0.89
C) $1.12
D) $1.13



StatusCorrectExplanation
correct.gif
Correct
BSince there are two known ratios (gallons per 3.79 liters and dollars per gallon), multiply them together so gallons will cancel out, and you will be left with the cost per liter. (1 gallon)/(3.79 liters) x $3.36/(1 gallon) = 0.887, so choice (B) is the correct answer.

Can you tell us where you have trouble understanding it? Otherwise, you're just asking us to say the same thing in a different way, without knowing what parts need to be changed.

Briefly, I might think this way: You are given two ratios that are equal to 1 (that is, numerator and denominator represent the same quantity):

3.79 liters/1 gallon, 3.36 dollars/1 gallon

You want the number of dollars per liter. So you want to multiply together fractions such that dollars will be on top (3.36 dollars/gallon is fine) and liters will be on the bottom (3.79 liters/gallon is upside-down).

So we can flip the second fraction: \(\displaystyle \displaystyle \frac{3.36\ \text{dollars}}{1\ \text{gallon}} \cdot \frac{1\ \text{gallon}}{3.79\ \text{liters}}\). The gallons will "cancel" just like when you multiply ordinary fractions, leaving \(\displaystyle \displaystyle\frac{3.36\ \text{dollars}}{3.79\ \text{liters}}\).

This means we divide 3.36 by 3.79, and the answer is 0.8865 dollars/liter, which rounds to $0.89.

Note that the wrong answers involve either dividing in the wrong order, or rounding incorrectly, so those appear to be the ideas they are testing.

This is not the only way to solve the problem; frankly, it is a good way largely because it does away with thinking! But another way to do it would be to think about the meaning of the ratios. We want the price for one liter. We know that 3.79 liters make a gallon; one liter is 1/3.79 of a gallon. We know that one gallon costs $3.36; 1/3.79 gallon costs 1/3.79 as much. So we have to multiply $3.36 by 1/3.79, which means dividing $3.36/3.79.

There are lots of other ways, so if you think of a way that makes sense to you because of your particular experiences, try it.
 
Madgod483 said:
A) $0.88
B) $0.89
C) $1.12
D) $1.13

If that section of that ASVAB test allows the use of a basic functions calculator, then I am okay with this problem/question.

However, if no calculators are allowed for this section, then I am not okay with this problem/question, because of the
combination of the time limit for the total number of questions, the amount of time to do the division here testing it out to a
third decimal place for the sake of rounding to two decimal places, and especially of how close the answer choices are.

For testing number sense (about what ballpark/size the end result should be), in part, the answer choices should not be made that
close to each other if a calculator would not be allowed.
 
Can you tell us where you have trouble understanding it? Otherwise, you're just asking us to say the same thing in a different way, without knowing what parts need to be changed.

Briefly, I might think this way: You are given two ratios that are equal to 1 (that is, numerator and denominator represent the same quantity):
3.79 liters/1 gallon, 3.36 dollars/1 gallon

You want the number of dollars per liter. So you want to multiply together fractions such that dollars will be on top (3.36 dollars/gallon is fine) and liters will be on the bottom (3.79 liters/gallon is upside-down).

So we can flip the second fraction: \(\displaystyle \displaystyle \frac{3.36\ \text{dollars}}{1\ \text{gallon}} \cdot \frac{1\ \text{gallon}}{3.79\ \text{liters}}\). The gallons will "cancel" just like when you multiply ordinary fractions, leaving \(\displaystyle \displaystyle\frac{3.36\ \text{dollars}}{3.79\ \text{liters}}\).

This means we divide 3.36 by 3.79, and the answer is 0.8865 dollars/liter, which rounds to $0.89.

Note that the wrong answers involve either dividing in the wrong order, or rounding incorrectly, so those appear to be the ideas they are testing.

This is not the only way to solve the problem; frankly, it is a good way largely because it does away with thinking! But another way to do it would be to think about the meaning of the ratios. We want the price for one liter. We know that 3.79 liters make a gallon; one liter is 1/3.79 of a gallon. We know that one gallon costs $3.36; 1/3.79 gallon costs 1/3.79 as much. So we have to multiply $3.36 by 1/3.79, which means dividing $3.36/3.79.

There are lots of other ways, so if you think of a way that makes sense to you because of your particular experiences, try it.


Actually this has answered my question. I was just having a hard time understanding how it was done, so I was just looking for someone to help break it down further as what you had just done.

Thank you so much!!
 
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