When Leo imported a certain item, he paid a 7 percent import

Question

Source: Official Guide 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? A. $1,600 B. $1,850 C. $2,250 D. $2,400 E. $2,750 The OA is C.

Brent@GMATPrepNow · Answer

BTGmoderatorLU wrote:Source: Official Guide 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? A. $1,600 B. $1,850 C. $2,250 D. $2,400 E. $2,750 The OA is C. When Leo imported a certain item, he paid a 7% import tax on the portion of the total value of the item in excess of $1000. If the amount of the import tax that Leo paid was $87.50 what was the total value of the item? A $1600 B $1850 C $2250 D $2400 E $2750 Here's a step-by-step algebraic solution. Let T = the TOTAL value of the item. Leo paid a 7% import tax on the portion of the total value of the item in EXCESS of $1000 So, Leo pays tax on the amount that's GREATER then $1000 So, Leo pays 7% tax on (T - 1000) We can write: import tax = 7% of (T - 1000) The amount of the import tax that Leo paid was $87.50 So, we write: $87.50 = 7% of (T - 1000) Or: $87.50 = 0.07(T - 1000) Expand to get: 87.50 = 0.07T - 70 Add 70 to both sides to get: 157.5 = 0.07T NOTE: At this point, you might just plug in the answer choices to see which one makes the above equation true. Or.... Divide both sides by 0.07 to get: 157.5/0.07 = T Solve: 2250 = T Answer: C Cheers, Brent

fskilnik@GMATH · Answer

BTGmoderatorLU wrote:Source: Official Guide 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? A. $1,600 B. $1,850 C. $2,250 D. $2,400 E. $2,750 $${\text{?}}\,\,{\text{ = }}\,\,{\text{total}}\,\,{\text{value}}\,\, = \,\,\$ \,\,\left( {1000 + {\text{extra}}} \right)$$ $${\text{87}}{\text{.5}}\,\,{\text{ = }}\,\,\frac{7}{{100}}\left( {{\text{extra}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{extra}}\,\,{\text{ = }}\,\,\frac{{{\text{100}}}}{7} \cdot \frac{1}{{10}}\left( {700 + 140 + 35} \right)\,\,\, = \,\,\,10 \cdot 125$$ $$? = \,1000 + 1250\,\,\,\left[ \$ \right]$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.

Scott@TargetTestPrep · Answer

BTGmoderatorLU wrote:Source: Official Guide 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? A. $1,600 B. $1,850 C. $2,250 D. $2,400 E. $2,750 The OA is C. We know that when Leo imported the item, he paid 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 did not pay any tax on his items until he hit $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; 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 Alternate Solution: Let’s let x = the portion of the item’s value on which he paid 7% tax. Thus, we have: 0.7x = 87.5 x = 1250 The taxable portion of the item was $1250, and the non-taxable portion was $1000. Therefore, the total value of the item is 1250 + 1000 = $2250. Answer: C

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