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When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?

When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?

Let the value of the item be \($x\), then \(0.07(x-1,000)=87.5\) --> \(x-1,000=1,250\) --> \(x=2,250\).

Answer: C.

Else, you could backsolve: If the value of the item is $2,000 the tax is \((2,000-1,000)*0.07=70\), so the value must be more than $2,000. Eliminate A and B. If the value of the item is $2,400 the tax is \((2,400-1,000)*0.07=98\), so the value must be less than $2,400. Eliminate D and E.

When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?

Let the value of the item be \($x\), then \(0.07(x-1,000)=87.5\) --> \(x-1,000=1,250\) --> \(x=2,250\).

Answer: C.

Else, you could backsolve: If the value of the item is $2,000 the tax is \((2,000-1,000)*0.07=70\), so the value must be more than $2,000. Eliminate A and B. If the value of the item is $2,400 the tax is \((2,400-1,000)*0.07=98\), so the value must be less than $2,400. Eliminate D and E.

Re: When Leo imported a certain item, he paid a 7 percent import [#permalink]

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18 Dec 2013, 10:21

Bunuel wrote:

SOLUTION

When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?

Let the value of the item be \($x\), then \(0.07(x-1,000)=87.5\) --> \(x-1,000=1,250\) --> \(x=2,250\).

Answer: C.

Else, you could backsolve: If the value of the item is $2,000 the tax is \((2,000-1,000)*0.07=70\), so the value must be more than $2,000. Eliminate A and B. If the value of the item is $2,400 the tax is \((2,400-1,000)*0.07=98\), so the value must be less than $2,400. Eliminate D and E.

Only answer choice C is left.

Do you have tips or a guide on how to most efficiently divide with non-integers in the denominator? I have seen two PS questions where they want us to divide some integer value with a non-integer (0.8 and now 0.07), and I do not really know how to properly approach the division.

When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?

Let the value of the item be \($x\), then \(0.07(x-1,000)=87.5\) --> \(x-1,000=1,250\) --> \(x=2,250\).

Answer: C.

Else, you could backsolve: If the value of the item is $2,000 the tax is \((2,000-1,000)*0.07=70\), so the value must be more than $2,000. Eliminate A and B. If the value of the item is $2,400 the tax is \((2,400-1,000)*0.07=98\), so the value must be less than $2,400. Eliminate D and E.

Only answer choice C is left.

Do you have tips or a guide on how to most efficiently divide with non-integers in the denominator? I have seen two PS questions where they want us to divide some integer value with a non-integer (0.8 and now 0.07), and I do not really know how to properly approach the division.

Re: When Leo imported a certain item, he paid a 7 percent import [#permalink]

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19 Dec 2013, 03:27

1

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Since we know Leo pays 7% of the amount that is in excess of $1000 We can assume 'x' to be the excess amount. Then 7 percent of x = 87.50 => x = 1250. Hence total value = 1000 + 1250 = 2250. Hence (C)

Re: When Leo imported a certain item, he paid a 7 percent import [#permalink]

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09 Sep 2014, 22:38

Bunuel wrote:

When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?

Re: When Leo imported a certain item, he paid a 7 percent import [#permalink]

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09 Sep 2014, 23:03

luckyme17187 wrote:

Bunuel wrote:

When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?

When Leo imported a certain item, he paid a 7 percent import [#permalink]

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11 May 2016, 07:18

Usually I do it the following way. If we are told that 7% of the excess amount is 87.5 then we can find the value of one 1%, i.e. 87.5/7=12.5. From this we can derive the full value of the excess amount: 12.5*100=1250=excess amount. 1000+1250
_________________

Re: When Leo imported a certain item, he paid a 7 percent import [#permalink]

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11 May 2016, 07:27

1

This post received KUDOS

Bunuel wrote:

When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?

Although this problem seems challenging it is actually a simple word translation.

We know that when Leo imports a certain item he pays a 7% import tax on the portion of the total value IN EXCESS OF $1,000. “In excess of” is the key phrase here, and it means that Leo does not pay any tax on his items until he hits $1,000. The best way to complete this problem is to set up an equation.

First, let’s say that T = total value of the item, and, therefore, (T – 1000) is the portion that is taxable.

Next, we can create an equation to determine T:

87.5 = 0.07(T – 1,000)

87.5 = 0.07T – 70

157.5 = 0.07T

157.5/0.07 = T

15,750/7 = T

T = 2,250

Answer C.
_________________

Jeffrey Miller Scott Woodbury-Stewart Founder and CEO

Re: When Leo imported a certain item, he paid a 7 percent import [#permalink]

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05 Jul 2016, 01:45

Bunuel wrote:

When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?

When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?

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