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.