SOLUTION: A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 70% salt and Solution B 95% is salt. She wants to o

Question 1129855: A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 70% salt and Solution B 95% is salt. She wants to obtain 70 ounces of a mixture that is 90% salt. How many ounces of each solution should she use?
solution A?
solution B?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = the number of ounces of the 70% solution.
y = the numberof ounces of the 95% solution.

x + y = 70
.7 * x + .95 * y = .9 * (x + y)

since x + y = 70, the second equation becomes:

.7 * x + .95 * y = .9 * 70 = 63

your two equations that need to be solved simultaneously are:

x + y = 70
.7 * x + .95 * y = 63

multiply both sides of the first equation by .7 and leave the second equation as is to get:

.7 * x + .7 * y = 49
.7 * x + .95 * y = 63

subtract the first equation from the second to get .25 * y = 14

solve for y to get y = 56

from x + y = 70, solve for x to get x = 14

your solution is x = 14 and y = 56.
that means that you need 14 ounces of the 70% solution and 56 ounces of the 95% solution to get 70 ounces of a 90% solution.

.7 * 14 + .95 * 56 = 63
63 / 70 = .9 = 90%

Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
.

Probably, it would be interesting for you to know that in the nature, the mixtures of the salt in water do not exist
at concentrations higher that 26% (weight to weight, or 350 grams per liter).

See this Wikipedia article
https://en.wikipedia.org/wiki/Saline_water

RELATED QUESTIONS
A scientist has two solutions, which she has labeled Solution A and Solution B. Each... (answered by richwmiller)
A scientist has two solutions, which she has labeled Solution A ad Solution B. Each... (answered by ikleyn)
A scientist has two solutions, which she has labeled Solution A and Solution B. Each... (answered by ewatrrr)
A scientist has two solutions,which she has labeled Solution A and B. Each contains... (answered by galactus,modi.kk91)
A scientist has two solutions, which she has labeled Solution A and Solution B. Each... (answered by robertb)
A scientist has two solutions, which she has labeled Solution A and Solution B. Each... (answered by scott8148)
A scientist has two solutions, which she has labeled Solution A and Solution B. Each... (answered by jorel1380)
A scientist has two solutions, which she has labeled Solution A and Solution B. Each... (answered by Maths68)
A scientist has two solutions, which she has labeled Solution A and Solution B. Each... (answered by Maths68)