Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
To make an orange dye, 3 parts of red dye are mixed with 2 parts of yellow dye. To make a green dye, 2 parts of blue dye are mixed with 1 part of yellow dye. If equal amounts of green and orange are mixed, what fraction of the new mixture is yellow dye?
(A) 3 /16
(B) 1 /4
(C) 11 /30
(D) 3/8
(E) 7 /12
The correct answer is C
Explanation
Suppose that x quarts of the final mixture of dye will be made. Since it is to be made from equal amounts of orange and green dye, it will consist of (1 over 2) times x quarts of orange dye and (1 over 2) times x quarts of green dye. Since the orange dye has 2 parts yellow dye for each 5 parts total dye, 2 over 5 of it is yellow dye. Similarly, 1 over 3 of the green dye is yellow dye. The amount of yellow in the final mixture is given by
((2 over 5) times (1 over 2) times x) + ((1 over 3) times (1 over 2) times x) = ((1 over 5) times x ) + ((1 over 6) times x)
= (11 over 30) times x quarts
So 11 over 30 of the final mixture is yellow dye.
Note: Although “quarts” were used to express the amount of the final mixture, it could have been pints or any other unit of liquid measure.