General Question

[estarkman1030]

I am taking a practice test and I am confused about one answer to a question...

"A clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 50 percent of what the collector had paid. The shop then sold the clock again at a profit of 80 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $100, for how much did the shop sell the clock the second time?


$270

$250

$240

$220

$200"

The explanation states that the answer is $270 for the following reason:

"If p is the price that the shop originally paid for the clock, then the price that the collector paid was 1.2p (to yield a profit of 20%). When the shop bought back the clock, it paid 50% of the sale price, or (.5)(1.2)p = .6p. When the shop sold the clock again, it made a profit of 80% on .6p or (1.8)(.6)p = 1.08p.

The difference between the original cost to the shop (p) and the buy-back price (.6p) is $100.
Therefore, p - .6p = $100. So, .4p = $100 and p = $250.

If the second sale price is 1.08p, then 1.08($250) = $270. (Note: at this point, if you recognize that 1.08p is greater than $250 and only one answer choice is greater than $250, you may choose not to complete the final calculation if you are pressed for time.)

The correct answer is A."

I do not understand how we arrived at 1.08 after this part "When the shop sold the clock again, it made a profit of 80% on .6p or (1.8)(.6)p = 1.08p."

Any advice?

Thanks

[StaceyKoprince]

Please read (and follow!) the forum guidelines before posting.

This folder is only for general strategy questions, not content or specific test problems. Check out the content / problem folders and post in the relevant folder depending upon the source of the problem you want to post (and make sure to follow the rules about banned sources). If you are a course student, you can also ask about other problems or issues before or after class or during section.

I'll answer quickly here, but in future, make sure to post in the correct folder.

First, the 1.8 came from "80% profit." 1 (or 100%) represents the original cost, so 80% profit on top of that is 1 + (1)(0.8) = 1.8.

Multiply that by the price 0.6p.
(1.8)(0.6)p = 1.08p
If you do that math (multiply together 1.8 and 0.6) the resulting number is 1.08. Do it on paper - try it out.

If you're not sure how to multiply two decimals, then you know you've got a skill you need to develop. You can look up how to do this in our Foundations of Math book or in whatever materials you're using to study for this test.