SOLUTION: A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 45% salt and Solution B is 95% salt. She wants to o
Algebra ->
Percentage-and-ratio-word-problems
-> SOLUTION: A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 45% salt and Solution B is 95% salt. She wants to o
Log On
Question 1204890: A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 45% salt and Solution B is 95% salt. She wants to obtain 90 ounces of a mixture that is 65% salt. How many ounces of each solution should she use? Found 2 solutions by math_tutor2020, josgarithmetic:Answer by math_tutor2020(3817) (Show Source):
A+B = 90
B = 90-A
0.45A = amount of pure salt from solution A
0.95B = amount of pure salt from solution B
0.45A+0.95B = total amount of pure salt
0.45A+0.95B = 90*0.65
0.45A+0.95(90-A) = 58.5
0.45A+0.95*90+0.95*(-A) = 58.5
0.45A+85.5-0.95A = 58.5
-0.5A + 85.5 = 58.5
-0.5A = 58.5 - 85.5
-0.5A = -27
A = -27/(-0.5)
A = 54
B = 90-A = 90-54 = 36
---------------------------------
Method 2
Solution A: 45%
Solution B: 95%
Target: 65%
The gap from 45% to 65% is 20
The gap from 65% to 95% is 30
The ratio 20:30 reduces to 2:3
We need 2 parts of one solution and 3 parts of another solution.
That scales up to 2x and 3x.
2x+3x = total amount of mixed solution
2x+3x = 90
5x = 90
x = 90/5
x = 18
2x = 2*18 = 36
3x = 3*18 = 54
We know from method 1 which value goes where, but if we didn't have that luxury then we'd have to check each case.
Case 1: We have 54 oz of A and 36 oz of B
Case 2: We have 36 oz of A and 54 oz of B
Case 1 leads to 54*0.45 + 36*0.95 = 58.5 oz of pure salt, which matches with the result of 90*0.65 = 58.5
This confirms the answers found in method 1.
Case 2 yields 36*0.45+54*0.95 = 67.5 oz of pure sault which doesn't match 90*0.65 = 58.5
We can eliminate this option.
=============================================================================
A scientist has two MIXTURES, which she has labeled MIXTURE A and MIXTURE B. Each contains salt. She knows that MIXTURE A is 45% salt and MIXTURE B is 95% salt. She wants to obtain 90 ounces of a mixture that is 65% salt. How many ounces of each A and B should she use?
=============================================================================
(