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A business must budget its money. Fractions for each part of one store's budget are listed below.

Which of the following comparisons is TRUE?

Attention Grabbers Bookstore Budget
Advertising 1/6
Rent 7/12
Supplies 1/4



A] The bookstore spends more on advertising than rent.


b} The bookstore spends more on supplies than advertising.


c}The bookstore spends more on advertising than supplies.


d]The bookstore spends more on supplies than rent.

User Pokemzok
by
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1 Answer

4 votes

Answer: Choice B

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Step-by-step explanation:

Let's go through each answer choice to see which are true and which are false.

A.

The fractions for advertising and rent are 1/6 and 7/12 respectively. The LCD is 12, so let's get 1/6 to have a denominator of 12. Multiply top and bottom by 2 to get 1/6 = 2/12.

Now we can compare the fractions 2/12 (aka 1/6) and 7/12. Clearly 7/12 is larger. It's like saying "having 7 slices of pizza is more than 2 slices of pizza". Therefore, the claim that more was spent on advertising compared to rent is false.

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B.

1/4 = 3/12 when multiplying top and bottom by 3

3/12 was spent on supplies and 2/12 was spent on advertising

We see that more was spent on supplies, so claim B is true

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C.

This claim is false because it contradicts claim B.

Another way to see why it's false is to use a calculator to get these decimal values

  • advertising = 1/6 = 0.17 approximately
  • supplies = 1/4 = 0.25 exactly

Since 0.17 is not larger than 0.25, this means 1/6 is not larger than 1/4.

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D.

We could use any of the methods mentioned in the previous sections, but I'll go another route.

For now assume that the fractions for supplies and rent (1/4 and 7/12 respectively) are equal.

Let's use cross multiplication to say the following:

1/4 = 7/12

1*12 = 4*7

12 = 28

Clearly the two sides are different so the original fractions aren't equal. To fix this error, replace each equal sign with a "less than" sign like so

1/4 < 7/12

1*12 < 4*7

12 < 28

Think of it like working backward up the chain. Start with 12 < 28 which is clearly true, and you can work backwards to end up with 1/4 < 7/12.

The fact we end up with 1/4 < 7/12 shows the claim "The bookstore spends more on supplies than rent" is false. It's the other way around: the bookstore spent more on rent compared to supplies.

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Summary: We found only choice B to be true. The other statements were false.

User Hunterjrj
by
6.7k points