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

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Question Stats: 74% (02:09) correct 26% (02:09) wrong based on 105 sessions

### HideShow timer Statistics 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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1
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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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

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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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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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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,  [#permalink]

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Bunuel 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) $$\frac{200n}{m}$$

(B) $$\frac{2n}{100m}$$

(C) $$\frac{2m}{n}$$

(D) $$\frac{2n}{m}$$

(E) $$200mn$$

Given the unit cost of pencil=20 cents=$0.2. Let the unit cost of pen$x.
Given, m pencils cost the same as n pens.
So, 0.2*m=n*x
Or, x=$$\frac{0.2m}{n}$$

Ans. (C)

So, cost of 10 pens=unit cost of pen * no of pens=x*10=$$\frac{0.2m}{n}*10$$=$$\frac{2m}{n}$$
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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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varun4s wrote:
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

Kudos please if you like my explanation!

Why both sides are multiplied by 10??
Intern  Joined: 24 Oct 2018
Posts: 10
Re: If m pencils cost the same as n pens, and each pencil costs 20 cents,  [#permalink]

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=> 11 pen

therefore 1010 pens

Given cost of 11 pencil

therefore cost of mm pencils =20m=20m cents

Option 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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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

We can let p = the cost of a pen, in cents and we can create the equation:

20m = pn

20m/n = p

So the cost of each pen, in dollars, is (20m/n)/100 = 20m/100n = m/5n.

So 10 pens cost:

10 x m/5n = 2m/n dollars.

Alternate Solution:

We are told that m pencils cost the same as n pens, and pencils cost 20 cents (0.20 dollars) each, so we have:

0.20m = n

We see that n pens cost 0.20m, so the cost of one pen can be obtained by dividing by n, so we get:

0.20m/n = n/n

0.20m/n = 1

Since 1 pen costs 0.20m/n dollars, then 10 pens costs (0.20m/n) x 10 = 2m/n dollars.

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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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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

pencil costs-20 cents
we have m pencils, so m pencil total cost=20m cents

20 m cost=n x - where n is no of pens

so 1 pen cost-20m/n cents
10-pen cost-200m/n cents
1 dollar=100 cents

so 10 pen cost-200m/n * 1/100=20m/n

correct OA:C
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Stay in the fight. Die another day! Re: If m pencils cost the same as n pens, and each pencil costs 20 cents,   [#permalink] 28 Oct 2018, 05:36
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