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Cake

by yellowho » Mon Feb 28, 2011 12:25 am
A certain bakery sells six di¤erent-sized wedding cakes. Each
cake costs x dollars more than the next one below it in size, and
the price of the largest cake is $24.50. If the sum of the prices of
the six di¤erent cakes is $109.50, what is the value of x?

K= first

Total equal=> 6k+15x=109.5
We know K+5x=24.5

Equation system=> solve for K then X=> X=12.5/5. Not part of the answer choices.
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by Anurag@Gurome » Mon Feb 28, 2011 1:44 am
Your approach is correct.
May be there is some problem with thee solution.
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by sanju09 » Mon Feb 28, 2011 1:45 am
yellowho wrote:A certain bakery sells six di¤erent-sized wedding cakes. Each
cake costs x dollars more than the next one below it in size, and
the price of the largest cake is $24.50. If the sum of the prices of
the six di¤erent cakes is $109.50, what is the value of x?

K= first

Total equal=> 6k+15x=109.5
We know K+5x=24.5

Equation system=> solve for K then X=> X=12.5/5. Not part of the answer choices.

Price of the largest cake = $24.50

Price of the next one below it in size = $24.50 - x

Price of the next one below it in size = $24.50 - 2 x

Price of the next one below it in size = $24.50 - 3 x

Price of the next one below it in size = $24.50 - 4 x

Price of the next one below it in size = $24.50 - 5 x

Total = 6 × $24.50 - (1 + 2 + 3 + 4 + 5) x = $109.50, GIVEN

Or 147 - 15 x = 109.50

Or 15 x = 37.5

Or x = [spoiler]2.5

Must be there in your choices[/spoiler]
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by sanju09 » Mon Feb 28, 2011 1:46 am
Anurag@Gurome wrote:Your approach is correct.
May be there is some problem with thee solution.
I don't think that his approach is correct
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by GMATGuruNY » Mon Feb 28, 2011 1:48 am
yellowho wrote:A certain bakery sells six di¤erent-sized wedding cakes. Each
cake costs x dollars more than the next one below it in size, and
the price of the largest cake is $24.50. If the sum of the prices of
the six di¤erent cakes is $109.50, what is the value of x?

K= first

Total equal=> 6k+15x=109.5
We know K+5x=24.5

Equation system=> solve for K then X=> X=12.5/5. Not part of the answer choices.
Sum of evenly spaced values = (Biggest + Smallest)/2 * (Number of values)

In the problem above:
Sum = 109.5
Biggest = 24.5
Smallest = 24.5 - 5x
Number of values = 6

Thus:
109.5 = (24.5 + 24.5 - 5x)/2 * 6
36.5 = 49 - 5x
5x = 12.5
x=2.5.

Even if we don't know the summation formula, we could solve easily by plugging in the answer choices, one of which would say x=2.5.

Answer choice: x=2.5
Then the cake prices would be 24.5, 22, 19.5, 17, 14.5, 12.
Sum = 24.5 + 22 + 19.5 + 17 + 14.5 + 12 = 109.5.
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by Anurag@Gurome » Mon Feb 28, 2011 1:59 am
sanju09 wrote:I don't think that his approach is correct
What he has done is same as yours, only the direction is different.

He has assumed the price of smallest cake as $K.
Hence, price of the cakes (in dollars) according to their increasing sizes are : K, (K + x), (K + 2x), (K + 3x), (K + 4x), and (K + 5x).

Hence, sum of the prices, (6K + 15x) = 109.50 ........... (I)
And, price of the largest cake, (K + 5x) = 24.50 .......... (II)

Solving these two above equations we can determine the value of x to be 2.50.
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by sanju09 » Mon Feb 28, 2011 2:04 am
Anurag@Gurome wrote:
sanju09 wrote:I don't think that his approach is correct
What he has done is same as yours, only the direction is different.

He has assumed the price of smallest cake as $K.
Hence, price of the cakes (in dollars) according to their increasing sizes are : K, (K + x), (K + 2x), (K + 3x), (K + 4x), and (K + 5x).

Hence, sum of the prices, (6K + 15x) = 109.50 ........... (I)
And, price of the largest cake, (K + 5x) = 24.50 .......... (II)

Solving these two above equations we can determine the value of x to be 2.50.
oh yeah, but he didn't mention it in the beginning that first means the smallest, that's why
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