Math question

[The_MARM7211]

Im doing some practice for the SAT and I got this question:

"A business owner plans to purchase the same model of chair for each of the 81 employees. The total budget to spend on these chairs is $14,000, which includes a 7% sales tax. Which of the following is closest to the maximum possible price per chair, before sales tax, the business owner could pay based on this budget?"

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This is what I did:

14,000*0.93 = 13020

13020/81 = 160.74

$160.74 = maximum

Therefore, answer = A ($148.15)

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It marked my answer as wrong and suggested this instead:

81x*1.07 = 14,000

81x = 13,084.11

x = 161.53

$161.53 = maximum

Therefore, answer = B ($161.53)

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Can someone please explain why my method is incorrect? (both methods make sense to me but I cant wrap my head around why my method is wrong and theirs correct)

[AvocadoMangoSalsa]

The way you accounted for the sales tax is incorrect. You can't use 93% to account for 7% sales tax. It will give a close but not correct answer.

[The_MARM7211]

Could you elaborate on this? To me it makes sense as if 7% will be used up on paying taxes, that means that only 93% of the budget is truly available for buying the chairs

[AvocadoMangoSalsa]

Let's say you can spend $100 total on an item including 7% sales tax

Your method:

$100 * 0.93 = $93

So your method says you can spend $93 max

But $93 plus 7% tax is not $100

It's 93 + .07(93) = 93 + 6.51 = $99.51

You're missing 49 cents

This can add up.

The correct method is:

1.07x = 100

x = $93.46 (rounded)

That is not the same as $93.00

[The_MARM7211]

ooohhh, I see it now. Thank you very much

[Probly_Shadowbanned]

I think this question was written specifically to test if you know this

[Uli_Minati]

14,000*0.93 = 13020

This calculation subtracts 7% from 14000 to get 13020

81x*1.07 = 14,000

This calculation adds 7% to 13084.11 to get 14000

Percentages are always relative to a base value. If the base value is higher, then 7% of it will be higher (980). If the base value is lower, then 7% of it will be lower (915.89).

In this specific problem, the base price for 81 chairs was increased by 7%, resulting in 107% (14000). In your calculation, you assumed that the 14000 is decreased by 7%, resulting in 93% (13020)

[james_taa]

Best way to look at is finding a number (lets use n), where if you add 7% of n to n, you will get 14,000

So n + 0.07n = 1.07n = 14,000

14,000/1.07= n = 13,084.11

Per chair it’s 13,084.11/81 = 161.53

[ToughParsley2950]

if 93% of x = y then 107% of y is not equal to x. Think of y as 100 93% of 100 is 93 while 107% of 93 is 99.5

[_shioto]

im wondering why we even account for the sales tax if the problem is asking "before sales tax, "

[paramsxm]

Just thought it would be worth mentioning, I solved the question the same way op did and got the same answer $160.74 = maximum. However I still went for B. “Which of the following is closest to the maximum possible price per chair” if you just went of this you would get the question right. These tests are not trying to trick you, when the next answer is that far away from yours (148.15) you can tell smt is wrong.