Question 1101215: Mr. Kang mixes an 85% sugar cinnamon-flavored solution with a 75% sugar cherry-flavored solution to make 20 gallons of a new product. The new product is 76% sugar. How much of the cherry-flavored solution did he use?
A.15 gal
B.2 gal
C.18 gal
D.20 gal
Found 4 solutions by richwmiller, greenestamps, josgarithmetic, amalm06:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! By substitution
We know the total amount is 20 gal,
We know the percentage of the total amount is 76%
We know the total amount has 15.2 gal. of 100%
We want to know the amount of cinnamon-flavored solution at 85%
We want to know the amount of cherry-flavored solution at 75%
x+y=20,
0.85*x+0.75*y=0.76*20
0.85*x+0.75*y=15.2
x=20-y
0.85*(20-y)+0.75*y=15.2
17-0.85y+0.75*y=15.2
-0.1*y=-1.8
We now know amount of cherry-flavored solution at 75%
y=18.0 gal. at 75%
x=20-y
We now know amount of cinnamon-flavored solution at 85%
x=2.0 gal. at 85%
check
0.85*2.0+0.75*18.0=0.76*20
1.7+13.5=15.2
15.2=15.2
ok
Apparently, alligation has been around since the 1950's. I am surprised it has not been taught as a standard method in more schools. I was not exposed to it.
Answer by greenestamps(13214)  (Show Source):
You can put this solution on YOUR website!
The other tutor provided a solution using a variation of the standard algebraic method for solving "mixture" problems.
There is a much easier method you can use, if you understand it.
Think of the percentages of the two ingredients and the final mixture on a number line: 75, 76, and 85.
The mixture percentage 76 is 1/10 of the distance from 75 to 85. (From 75 to 85 is 10; from 75 to 76 is 1.)
That means 1/10 of the mixture must be the 85% ingredient. With a total of 20 gallons of the mixture, that means 2 gallons.
Answer: use 2 gallons of the 85% sugar cinnamon-flavored solution and 18 gallons of the 75% sugar cherry flavored solution.
Answer by josgarithmetic(39630)  (Show Source):
Answer by amalm06(224)  (Show Source):
You can put this solution on YOUR website! Using the method of alligation,
Let CH=0.75 and S=0.85
Then 0.76-075=0.1 and 0.85-0.76=0.09
So that CH/S=0.09/0.1
Thus, there are 0.09 parts of cherry-flavored solution for every 0.1 parts of mixture
If there are 20 parts of mixture, then (0.09/0.10)(20)=18 gallons of cherry-flavored solution (Answer)
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