dzodzo85 wrote:
John purchased large bottles of water for $2 each and small bottles of water for $1.50 each. What percent of the bottles purchased were small bottles?
(1) John spent $33 on the bottles of water
(2) The average price of bottles purchased was $1.65
We are given that John purchased large bottles of water for $2 each and small bottles of water for $1.50 each. We can let s = the number of small bottles purchased, and b = the number of larger bottles purchased. We need to determine what percentage of the bottles purchased were small bottles, i.e. the value of s/(s+b) x 100.
Statement One Alone:
John spent $33 on the bottles of water.
Using the information in statement one, we can create the following equation:
2b + 1.5s = 33
We can multiply the entire equation by 2 and we have:
4b + 3s = 66
4b = 66 - 3s
4b = 3(22 - s)
b = [3(22 - s)]/4
Since b must be an integer, 3(22 - s) must be a multiple of 4.
3(22 - s) is a multiple of 4 when s = 2, 6, 10, 14, or 18.
Since we have multiple values of s, we will also have multiple values of b, and thus we do not have enough information to answer the question.
Statement Two Alone:
The average price of bottles purchased was $1.65.
Using the information in statement two, we can create the following equation:
1.65 = (2b + 1.5s)/(b + s)
1.65(b + s) = 2b + 1.5s
165(b + s) = 200b + 150s
165b + 165s = 200b + 150s
15s = 35b
3s = 7b
(3/7)s = b
We can now determine the value of s/(s+b) x 100 by substituting (3/7)s for b:
s/[s+(3/7)s] x 100
s/[(10/7)s] x 100
1/(10/7) x 100
7/10 x 100 = 70
So the small bottles account for 70 percent of the bottles purchased. We have answered the question.
Answer: B
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51% (01:25) correct 
