nafiul9090 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?
(A) 1.50
(B) 1.75
(C) 2.00
(D) 2.50
(E) 3.00
is there any short cut method??
The prices are evenly spaced values.
With evenly spaced values, median = average = sum/number.
Thus, the median price of the cakes = (109.5)/6 = 18.25.
We can plug in the answer choices, which represent the distance between consecutive prices.
The median of 18.25 must be halfway between the 3rd greatest price and the 4th greatest price.
Answer choice C: 2
4th greatest price = 24.5 - 2(2) = 20.5, 3rd greatest price = 20.5 - 2 = 18.5.
18.25 is not halfway between 18.5 and 20.5.
The difference between consecutive prices must be greater.
Eliminate A, B and C.
Answer choice D: 2.5
4th greatest price = 24.5 - 2(2.5) = 19.5, 3rd greatest price = 19.5 - 2.5 = 17.
Success! 18.25 is halfway between 17 and 19.5.
The correct answer is
D.
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