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Director  Joined: 01 May 2007
Posts: 751
At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes,  [#permalink]

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14 00:00

Difficulty:   75% (hard)

Question Stats: 45% (01:12) correct 55% (01:06) wrong based on 182 sessions

HideShow timer Statistics At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $120. At the same place it would cost$164.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola?

A. $21 B.$27
C. $31 D.$41
E. It cannot be determined

This is a challenge problem, but from the FREE PRACTICE BIN, so don't freak out on my for posting a challenge problem on the forum. I've never seen this type of explanation before. I always assumed that if you had 3 variables, you needed 3 equations to solve. I've also never seen a solution where you subtract multiple times from the same equation. Is this even kosher? Is there a way to solve this without subtracting multiple times by the same #?

Explanation

Let's suppose that the price of burger is $B, of shake$S and cola's price is $C. We can then construct equations: {3B+7S+C=$120
{4B+10S+C=$164.5 Subtracting first equation from the second, gives us B+3S=$44.5.
Now if we subtract new equation two times from first or 3 times from second we will get B+S+C=$31. In any case, there is no necessity to know each items price, just the sum. M00-01 Manager  Joined: 27 May 2007 Posts: 119 Re: At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, [#permalink] Show Tags That's really helpful! I've never seen that type of solution before either, but there's no reason why it shouldn't work. If B+32=$44.50 is a true statement, there's no reason why it couldn't be applied as many times as needed to get to the answer.
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Re: At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes,  [#permalink]

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10
6
3B + 7S + 1C = 120
4B + 10S + 1C = 164.50

Subtracting 1 from 2

B + 3S = 44.50

Now MULTIPLY ABOVE by 2

2B + 6S = 89

First equation can be written as:

B + 2B+6S + S + C = 120

OR

B + S + C + 89 = 120

B + S + C = 31
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Re: At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes,  [#permalink]

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1
anceer wrote:
At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $120. At the same place it would cost$164.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola?
A $21 B$27
C $31 D$41
E It cannot be determined

price of one burger=x, price of one shake= y, and price of one cola= z

3x+7y+z = 120------------1)
4x+10y+z=164.5-------------2)

subtracting 1 from 2 we have
x+3y=44.5

now multiply both sides by 3,
3x+9y=133.5------------------3)

from 2 we have
x+3x +9y+y+z=164.5
substitute the value of 3x+9y in 3 we have
x+y+z=164.5-133.5
=31
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Re: At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes,  [#permalink]

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3b + 7s + 1c = 120 ......... (1)

4b + 10s + 1c = 164.5 ........ (2)

(2) - (1)

1b + 3s = 44.5

3b + 9s = 44.5*3 .............. (3)

Rearranging equation (2)

(3b + 9s) + (1a + 1s + 1c) = 164.5

1a + 1s + 1c = 164.5 - 133.5 = 31

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At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes,  [#permalink]

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2
2
jimmyjamesdonkey wrote:
At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $120. At the same place it would cost$164.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola?

A. $21 B.$27
C. $31 D.$41
E. It cannot be determined

This is a challenge problem, but from the FREE PRACTICE BIN, so don't freak out on my for posting a challenge problem on the forum. I've never seen this type of explanation before. I always assumed that if you had 3 variables, you needed 3 equations to solve. I've also never seen a solution where you subtract multiple times from the same equation. Is this even kosher? Is there a way to solve this without subtracting multiple times by the same #?

Explanation

Let's suppose that the price of burger is $B, of shake$S and cola's price is $C. We can then construct equations: {3B+7S+C=$120
{4B+10S+C=$164.5 Subtracting first equation from the second, gives us B+3S=$44.5.
Now if we subtract new equation two times from first or 3 times from second we will get B+S+C=$31. In any case, there is no necessity to know each items price, just the sum. :evil: M00-01 At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for$120. At the same place it would cost $164.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola? A.$21
B. $27 C.$31
D. \$41
E. It cannot be determined

Let's suppose that the price of a burger is $$B$$, of a shake - $$S$$ and that of a cola is $$C$$. We can then construct these equations:
$$3B+7S+C = 120$$
$$4B+10S+C = 164.5$$

Subtracting the first equation from the second gives us $$B+3S=44.5$$.

Now if we subtract the new equation two times from first or 3 times from second we will get $$B+S+C=31$$. In any case, there is no necessity to know each item's price, just the sum.

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Re: At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes,  [#permalink]

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_________________ Re: At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes,   [#permalink] 27 Aug 2018, 01:48
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