Vincen wrote: ↑Thu Nov 26, 2020 1:02 pm
Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 50% nuts, what percent of the combined mixture is dried fruit?
A) 16.67%
B) 23.33%
C) 25%
D) 33.33%
E) 36.67%
Answer:
B
Source: Veritas Prep
Let's say that the combined mixture weighs
100 pounds.
If the combined mix is 50% nuts, then there are
50 pounds of nuts in the combined mixture.
Let's let x = the # of pounds of Sue's trail mix
This means that
100-x = the # of pounds of Jane's trail mix
My word equation:
(# of pounds of nuts in Sue's portion) + (# of pounds of nuts in Jane's portion) = 50
In other words: (30% of x) + (60% of
100-x) =
50
Rewrite as: 0.3x + 0.6(
100-x) =
50
Expand: 0.3x + 60 - 0.6x =
50
Simplify: -0.3x = -10
Solve: x = 10/0.3 = 100/3 =
33 1/3
In other words, the combined (
100-pound) mixture contains
33 1/3 pounds of Sue's trail mix.
If Sue's trail mix is 70% dried fruit, then the total weight of dried fruit = (0.7)(
33 1/3) = 23 1/3
So, of the
100 pounds of combined mix, there are 23 1/3 pounds of dried fruit.
In other words, 23 1/3% of the combined mixture is dried fruit?
Answer: B
Cheers,
Brent
