Bunuel wrote:
In the first hour of a bake sale, students sold either chocolate chip cookies, which sold for $1.30, or brownies, which sold for $1.50. What was the ratio of chocolate chip cookies sold to brownies sold during the first hour of the bake sale?
(1) The average price for the items sold during that hour was $1.42 --> \(\frac{1.30c+1.50b}{c+b}=1.42\) --> \(8b=12c\) --> \(\frac{c}{b} = \frac{2}{3}\). Sufficient.
(2) The total price for all the goods sold was $14.20. This statement is a bit trickier: \(1.30c+1.50b=14.20\) --> \(13c+15b=142\). Since c and b must be integers, then we should check whether this equation has one or more than one positive integer solutions: \(15b=142-13c\) --> 142 minus multiple of 13 must be a multiple of 15: only c=4 and b=6 satisfies the equation, thus \(\frac{c}{b} = \frac{4}{6}\). Sufficient.
Answer: D.
Hope it helps.
Hi
BunuelFor S2 -- How did you know c =4 and b = 6 is the ONLY integers that work for this equation ?
I got c = 4 and b = 6 AND STILL chose insufficient because i thought there MAYBE more integers that i have not tested
I could NOT test it because i ran out of time and i had to move on
Please confirm how does one ensure c =4 and b = 6 is the ONLY solution to this equation without testing a huge number of integers