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The average price of an antique car

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by BTGmoderatorDC » Wed Oct 11, 2017 2:38 am
The average price of an antique car increases over the years. If from 1990 to 1996, the price of the car increased by 13% and from 1996 to 2001 it increased by 20%, what is the price of the car in 2001 if the price in 1990 was $11,500?

A. $15,594.
B. $15,322.
C. $14,786.
D. $14,543.
E. $12,988.

How can i formulate a solution to this?Where should i start?

OA A
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by ErikaPrepScholar » Wed Oct 11, 2017 8:35 am
Hey lheiannie07,

My first step here would be to write out what I know on my scratch paper:

1990: $11,500
+13%
1996: ?
+20%
2001: ?

We want to solve for the price in 2001. We know how much the car cost in 1990, so let's start there. From 1990 to 1996, the price increased 13%. This means that the price in 1996 is 113% of the price in 1990. Converting that into a decimal, we get that price in 1996 = 1.13(price in 1990) or price in 1996 = 1.13($11,500). Solving that gives $12,995. We can fill that in on our scratch paper:

1990: $11,500
+13%
1996: $12,995
+20%
2001: ?

Now we can use the price in 1996 to find the price in 2001. From 1996 to 2001, the price increased 20%. This means that the price in 2001 is 120% of the price in 1996. Again, converting that into a decimal, we get that price in 2001 = 1.2(price in 1996) or price in 2001 = 1.2($12,995). Solving that gives $15,594. So the price of the car in 2001 is $15,594, making A the correct answer.
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by Matt@VeritasPrep » Wed Oct 11, 2017 5:25 pm
11500 * 1.13 * 1.2 =>

11500 * 1.13 * (6/5) =>

13800 * 1.13 =>

13800 * (1 + .13) =>

13800 + 13800 * .13 =>

13800 + 13800 * (≈1/8) =>

≈ 13800 + 1725 =>

≈ 15525

A's the closest, so we'll go with that!
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by Matt@VeritasPrep » Wed Oct 11, 2017 5:27 pm
Here's another trick:

11500 * 1.13 * 1.2 =>

13800 * 1.13

From here, notice that .03 * 800 = 24, so our answer MUST end in a 4. Only A fits, so we're done!
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by Matt@VeritasPrep » Wed Oct 11, 2017 5:29 pm
Of course, we could also punish ourselves and find the exact answer. My usual approach is to chop the percentages into friendlier pieces, like 1% and 10%. For example:

11500 * 1.13 =>

11500 * (1 + .1 + .01 + .01 + .01) =>

11500 + 1150 + 115 + 115 + 115 =>

12995

Now we've got to multiply this by 1.2, for the 20% increase:

12995 * (1 + .1 + .1) =>

12995 + 1299.5 + 1299.5 =>

15594

The addition is more tedious than the multiplication, but it does get us there eventually.
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Re: The average price of an antique car

by Scott@TargetTestPrep » Thu Jan 23, 2020 9:24 am
BTGmoderatorDC wrote: ↑
Wed Oct 11, 2017 2:38 am
 The average price of an antique car increases over the years. If from 1990 to 1996, the price of the car increased by 13% and from 1996 to 2001 it increased by 20%, what is the price of the car in 2001 if the price in 1990 was $11,500?

A. $15,594.
B. $15,322.
C. $14,786.
D. $14,543.
E. $12,988.

How can i formulate a solution to this?Where should i start?

OA A
The price of the car in 2001 is:

11,500 x 1.13 x 1.2 = $15,594

Answer: A

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