aaggar7 wrote: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%
Here's one approach.
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 = 33.3333..
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) = [spoiler]23 1/3[/spoiler]
So, of the
100 pounds of combined mix, there are [spoiler]23 1/3 [/spoiler]pounds of dried fruit.
In other words, [spoiler]23 1/3%[/spoiler] of the combined mixture is dried fruit.
Answer:
B
Cheers,
Brent
