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If m pencils cost the same as n pens, and each pencil costs 20 cents,

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If m pencils cost the same as n pens, and each pencil costs 20 cents,  [#permalink]

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New post 26 Sep 2017, 17:50
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If m pencils cost the same as n pens, and each pencil costs 20 cents, what is the cost, in dollars, of 10 pens, if each pen costs the same amount? (100 cents = 1 dollar)

A. 200n/m

B. 2n/100m

C. 2m/n

D. 2n/m

E. 200nm

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Re: If m pencils cost the same as n pens, and each pencil costs 20 cents,  [#permalink]

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New post 26 Sep 2017, 19:27
equality
20*m=n*x (x price of pens)
multiply the equality by 10
10*20*m=10*n*x
200m=10nx
10x=200m/n or in dollars 2m/n
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Re: If m pencils cost the same as n pens, and each pencil costs 20 cents,  [#permalink]

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New post 26 Sep 2017, 20:15
Let cost of each pen= y
No of pens= n
Total cost of pen= ny

Cost of each pencil= 20 cents
No of pencils= m
Total cost of pencil= 20m

Total cost of m pencils= Total cost of n pens
20m=ny
Multiply both sides by 10
200m= 10ny
10y =\(\frac{200m}{n}\)
10y= \(\frac{2m}{n}\) (100cents= 1 dollar)
cost of 10 pencils= 10y

Answer:C.

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Re: If m pencils cost the same as n pens, and each pencil costs 20 cents,  [#permalink]

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New post 26 Sep 2017, 21:23
Gnpth wrote:
If m pencils cost the same as n pens, and each pencil costs 20 cents, what is the cost, in dollars, of 10 pens, if each pen costs the same amount? (100 cents = 1 dollar)

A. 200n/m

B. 2n/100m

C. 2m/n

D. 2n/m

E. 200nm


Given: \(n\) pens \(= m\) pencils

=> \(1\) pen \(= \frac{m}{n}\) pencils

therefore \(10\) pens \(= \frac{10m}{n}\) pencils

Given cost of \(1\) pencil = \(20\) cents

therefore cost of \(m\) pencils \(= 20m\) cents

hence cost of \(10\) pens in \($ = \frac{(10*20m)}{n}*\frac{1}{100} = \frac{2m}{n}\)

Option C
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If m pencils cost the same as n pens, and each pencil costs 20 cents,  [#permalink]

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New post 26 Sep 2017, 22:14
The cost of m pencils is the same as the cost of n pens.
Assume m = 5 and n = 4
Let x be the cost of a pen.

Given data: Cost of a pencil - 20 cents

20m = nx
20*5 = 4*x => x = 5*5 = 25 cents
Therefore, if each pencil costs 20 cents, the pens cost 25 cents.

We have been asked to find the cost of 10 pens in dollars,
the cost of 10 pens will be 250 cents or 2.5$

Putting the values of m and n in the answer options, we will be able to arrive at the solution

A. \(\frac{200n}{m} = \frac{200*4}{5} = 250\)$(wrong)
B. \(\frac{2n}{100m} = \frac{2 * 5}{100 * 4} = \frac{1}{40} = 0.25\)$(wrong)
C. \(\frac{2m}{n} = \frac{2*5}{4} = 2*1.25 = 2.5\)$(correct)

Hence, Option C is the correct answer option.
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If m pencils cost the same as n pens, and each pencil costs 20 cents, &nbs [#permalink] 26 Sep 2017, 22:14
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