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# If w widgets cost c cents, how many widgets can you get for d dollars?

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Math Expert
Joined: 02 Sep 2009
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If w widgets cost c cents, how many widgets can you get for d dollars?  [#permalink]

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04 Sep 2018, 23:10
00:00

Difficulty:

35% (medium)

Question Stats:

69% (01:08) correct 31% (01:06) wrong based on 67 sessions

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If w widgets cost c cents, how many widgets can you get for d dollars?

(A) $$\frac{100dw}{c}$$

(B) $$\frac{dw}{100c}$$

(C) $$100cdw$$

(D) $$\frac{dw}{c}$$

(E) $$cdw$$

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Re: If w widgets cost c cents, how many widgets can you get for d dollars?  [#permalink]

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05 Sep 2018, 01:00
Bunuel wrote:
If w widgets cost c cents, how many widgets can you get for d dollars?

(A) $$\frac{100dw}{c}$$

(B) $$\frac{dw}{100c}$$

(C) $$100cdw$$

(D) $$\frac{dw}{c}$$

(E) $$cdw$$

Unit cost of widgets=$$\frac{c}{w}$$ cents
Or, $$\frac{c}{100w}$$ dollars are required to purchase 1 widget
Or, $1 is required to purchase $$\frac{100w}{c}$$widgets hence$d is required to purchase $$\frac{100dw}{c}$$

Ans. (A)
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Re: If w widgets cost c cents, how many widgets can you get for d dollars?  [#permalink]

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05 Sep 2018, 01:30
For c cents, w widgets can be bought

......1 cent.., $$\frac{w}{c,}$$ widgets can be bought

.......100d cents...., $$\frac{w}{c}$$*100d widgets can be bought

= $$\frac{100dw}{c}$$

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If w widgets cost c cents, how many widgets can you get for d dollars?  [#permalink]

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15 Sep 2018, 08:40
One of my favorite approaches for questions with all variables is plug-in method.

Let w=100 pcs, c=100 cents, d = \$1 (actually d=c, so for 'd' we can buy the same number of 100 pcs - now we have to find an option that will give us the same 100 pcs.). Only option A gives us 100. Hence this is the right choice.

Now if you wonder how efficient this method is: 01:10 for the question above and I got the right answer, with my brain in a low level of energy consumption mode. Belive me, the saved brain stamina will be very useful for hard level questions later on the test. I highly recommend to use algebra only in cases in which it is really necessary.
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Re: If w widgets cost c cents, how many widgets can you get for d dollars?  [#permalink]

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15 Sep 2018, 08:51
Bunuel wrote:
If w widgets cost c cents, how many widgets can you get for d dollars?

(A) $$\frac{100dw}{c}$$

(B) $$\frac{dw}{100c}$$

(C) $$100cdw$$

(D) $$\frac{dw}{c}$$

(E) $$cdw$$

1 Dollar = 100 Cents

So, d Dollar = 100 d Cents

For c cents w widgets can be bought

So, For 1 cents $$\frac{w}{c}$$ widgets can be bought

Thus, for 100 d Cents $$\frac{100dw}{c}$$ widgets can be bought, Answer must be (A)
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Re: If w widgets cost c cents, how many widgets can you get for d dollars? &nbs [#permalink] 15 Sep 2018, 08:51
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