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A vendor sells h hot dogs and s sodas. If a hot dog costs twice as muc

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Math Expert
Joined: 02 Sep 2009
Posts: 56256
A vendor sells h hot dogs and s sodas. If a hot dog costs twice as muc  [#permalink]

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05 Jul 2018, 21:43
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45% (medium)

Question Stats:

67% (02:03) correct 33% (01:53) wrong based on 38 sessions

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A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does soda costs?

A. $$\frac{100d}{(s +2h)}$$

B. $$\frac{(s + 2h)}{100d}$$

C. $$\frac{d(s +2h)}{100}$$

D. $$\frac{d}{(100s +2h)}$$

E. $$\frac{d}{100(s + 2h)}$$

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Re: A vendor sells h hot dogs and s sodas. If a hot dog costs twice as muc  [#permalink]

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05 Jul 2018, 22:49
Bunuel wrote:
A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does soda costs?

A. $$\frac{100d}{(s +2h)}$$

B. $$\frac{(s + 2h)}{100d}$$

C. $$\frac{d(s +2h)}{100}$$

D. $$\frac{d}{(100s +2h)}$$

E. $$\frac{d}{100(s + 2h)}$$

d \$=d*100 cent

Let the unit cost of soda be p cents. So, unit cost of hot dog=2p cents

Total cost=cost of hot dog+cost of soda
or, 100d=h*2p+s*p=p(2h+s)
Or, $$p=\frac{100d}{(s+2h)}$$

Ans. (A)
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Joined: 02 Aug 2009
Posts: 7764
Re: A vendor sells h hot dogs and s sodas. If a hot dog costs twice as muc  [#permalink]

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05 Jul 2018, 23:28
Bunuel wrote:
A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does soda costs?

A. $$\frac{100d}{(s +2h)}$$

B. $$\frac{(s + 2h)}{100d}$$

C. $$\frac{d(s +2h)}{100}$$

D. $$\frac{d}{(100s +2h)}$$

E. $$\frac{d}{100(s + 2h)}$$

a quick method...
d is in dollars but we are asking in cents so d dollar = 100d in cents
so keep the choices that have 100d together
Only A and B
Now we are looking for amount so amount that is 100d should be in numerator
B gives us something per cent, not what we are looking for
A

algebraic method
let soda cost x, then hot dog costs 2x
total cost $$= sx+2hx=x(s+2h)=100d...............x=\frac{100d}{s+2h}$$
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Re: A vendor sells h hot dogs and s sodas. If a hot dog costs twice as muc  [#permalink]

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13 Jul 2018, 14:20
Bunuel wrote:
A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does soda costs?

A. $$\frac{100d}{(s +2h)}$$

B. $$\frac{(s + 2h)}{100d}$$

C. $$\frac{d(s +2h)}{100}$$

D. $$\frac{d}{(100s +2h)}$$

E. $$\frac{d}{100(s + 2h)}$$

We can let the cost of a soda = x cents; thus, the cost of a hot dog = 2x cents. Since d dollars = 100d cents, we can create the following equation:

2xh + xs = 100d

x(2h + s) = 100d

x = 100d/(2h + s)

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Re: A vendor sells h hot dogs and s sodas. If a hot dog costs twice as muc   [#permalink] 13 Jul 2018, 14:20
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