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Last Monday a certain store sold 17 wrenches at x dollars ea

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Last Monday a certain store sold 17 wrenches at x dollars ea [#permalink] New post 11 Dec 2017, 10:07
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Last Monday a certain store sold 17 wrenches at x dollars each. Last Tuesday the store reduced its prices and sold an additional 8 wrenches at 0.5x dollars each. Which of the following is equal to the average (arithmetic mean) price, in dollars, of the 25 wrenches that the store sold last Monday and Tuesday?

A. 0.68x
B. 0.73x
C. 0.76x
D. 0.81x
E. 0.84x
[Reveal] Spoiler: OA

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Re: Last Monday a certain store sold 17 wrenches at x dollars ea [#permalink] New post 02 Feb 2018, 19:33
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There are a couple of ways to do this problem. My favorite is called the RAF shortcut. It's amazing. But since this is a relatively simple problem I'll just algebra for this one. If there is any interest I can do a follow-up post on the RAF shortcut.

Anyway, we want to find total sales for this wrench. On Monday, the store sold 17 at x dollars each, which totals 17x dollars. On Tuesday, similarly, they sold 8 at .5x each, which totals 4x dollars. So the total revenue must be 17x + 4x = 21x. Total wrenches sold were 25.

According to the average formula, Sum/# of items = Average, so if we divide 21x by 25 we should get the average. But what's 21x/25? It doesn't look like any of the answer choices, which are all in decimal. And nobody wants to divide 21 by 25. Fortunately there's a trick. There's always a trick. If you ever need to convert a fraction into a decimal, try to make the denominator into some factor of 10, like 10, 1000, 1000000, etc. Then we can easily divide the numerator by the denominator by simply sliding the decimal over. In this case, if we multiply the denominator by 4, we'd get 100. So we multiply both the numerator and denominator by 4 (you can't multiply just one, but you can always multiply both as long as it's the same number; it's like the opposite of cancelling). This should get us 84x/100. Then we can just divide 84 by 100 to get .84x. So the answer is E.
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Re: Last Monday a certain store sold 17 wrenches at x dollars ea [#permalink] New post 03 Feb 2018, 03:55
Thank you.
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Re: Last Monday a certain store sold 17 wrenches at x dollars ea [#permalink] New post 10 Mar 2018, 23:52
Carcass wrote:
Last Monday a certain store sold 17 wrenches at x dollars each. Last Tuesday the store reduced its prices and sold an additional 8 wrenches at 0.5x dollars each. Which of the following is equal to the average (arithmetic mean) price, in dollars, of the 25 wrenches that the store sold last Monday and Tuesday?

A. 0.68x
B. 0.73x
C. 0.76x
D. 0.81x
E. 0.84x


Why do the additional 8 wrenches does not mean 17+8=25, this is what i interpreted and solved to get the answer, why was i wrong?
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Re: Last Monday a certain store sold 17 wrenches at x dollars ea [#permalink] New post 14 Mar 2018, 00:31
Let x = $10 so 0.5x = $5.

Mon: 17 wrenches sold and each costs $10 so the total cost is $170.

Tue: 8 wrenches sold and each costs $5 so the total cost is $40.

So the average of the 25 wrenches sold is $(170 + 40)/25 = $8.4.

Now try plugging in x=$10 to the answers to see if you get $8.4. Only E works so it is the answer.
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Re: Last Monday a certain store sold 17 wrenches at x dollars ea [#permalink] New post 29 May 2018, 06:51
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Carcass wrote:
Last Monday a certain store sold 17 wrenches at x dollars each. Last Tuesday the store reduced its prices and sold an additional 8 wrenches at 0.5x dollars each. Which of the following is equal to the average (arithmetic mean) price, in dollars, of the 25 wrenches that the store sold last Monday and Tuesday?

A. 0.68x
B. 0.73x
C. 0.76x
D. 0.81x
E. 0.84x


The average is:

(17x + 8(0.5x))/25 = 21x/25 = 84x/100 = 0.84x

Answer: E
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Re: Last Monday a certain store sold 17 wrenches at x dollars ea   [#permalink] 29 May 2018, 06:51
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