SOLUTION: One solution contains 2 parts salt to 8 parts water, and another contains 3 parts salt to 5 parts water. How much of each should be mixed together in order to obtain 280 quarts of

Question 1107081: One solution contains 2 parts salt to 8 parts water, and another contains 3 parts salt to 5 parts water. How much of each should be mixed together in order to obtain 280 quarts of a solution that is 3 parts salt to 7 parts water?
ANSWER: __ quarts and ____ quarts respectively
Thanks for helping! <3
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let's convert these solutions to percent salt
:
One solution contains 2 parts salt to 8 parts water, and
solution a: 2/10 = .2 solution is 20% salt
:
another contains 3 parts salt to 5 parts water.
solution b: 3/8 = .375 solution is 37.5% salt
:
How much of each should be mixed together in order to obtain 280 quarts of a solution that is 3 parts salt to 7 parts water?
3/10 = .30 resulting solution is 30% salt
:
A mixture equation in decimal form
.2a + .375b = .30(280)
a + b = 280
a = 280 - b
In the 1st equation replace a with (280-b)
.2(280-b) + .375b = .30(280)
56 - .2b + .375b = 84
.175b = 84 - 56
.175b = 28
b =
b = 160 qts of 37.5% solution (3:5
then
280 - 160 = 120 qts of the 20% solution (2:8)
:
:
Check:
.2(120) + .375(160) = .3(280)
24 + 60 = 84

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