SOLUTION: How many cups of a 15 % salt mixture and a 55 % salt mixture should you mix to get 4 cups of a 45 % salt mixture?

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Question 1126215: How many cups of a
15
%
salt mixture and a
55
%
salt mixture should you mix to get
4
cups of a
45
%
salt mixture?
Found 3 solutions by josgarithmetic, greenestamps, Alan3354:
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
"Mixture", is good. (But "solution" would not be good.)
These could be dry physical mixes.

---
How many cups of a
15
%
salt mixture and a
55
%
salt mixture should you mix to get
4
cups of a
45
%
salt mixture?
---

x of the 55% mixture
4-x of the 15% mixture
15%284-x%29%2B55x=45%2A4
-
55x%2B60-15x=180
40x=180-60
40x=120
highlight%28x=3%29--------- 3 cups of the 55%
-
highlight%281%29---------------------- cup of the 15%

Answer by greenestamps(13196) About Me  (Show Source):
You can put this solution on YOUR website!


You are likely to get a response from one or more tutors here who will tell you the problem can't be solved because a 55% salt solution is physically impossible.

However, this is a math site and not a Chemistry site; clearly the intention of the problem was to give you practice in solving mixture problems. So let's do that.

First a solution by the traditional algebraic method.

let x = the number of cups of 15% solution
then 4-x = the number of cups of 55% solution

We want the 4 cups of mixture to be a 45% solution. So 15% of the x cups, plus 55% of the (4-x) cups, equals 45% of the 4 cups:

.15%28x%29%2B.55%284-x%29+=+.45%284%29
.15x%2B2.2-.55x+=+1.8
0.4+=+0.4x
x+=+1

ANSWER: The mixture should use 1 cup of the 15% solution and 3 cups of the 55% solution.

Now a very different method which, as you will see, requires much less work.

(1) Think of the three percentages on a number line -- 15, 45, and 55.
(2) 45 is 3/4 of the way from 15 to 55. (do some simple mental arithmetic)
(3) That means 3/4 of the mixture must be the 55% solution.
(4) 3/4 of the total 4 cups is 3 cups.

ANSWER: 3 cups of the 55% solution, 1 cup of the 15% solution.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Re: greenestamps' statement about 55% salt:
While the salt NaCl might not be soluble to 55%, other salts might be.
There are a lot of salts.
-----------
Also, it wasn't specified salt in water.