Question 1204890
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Answers:
<font color=red>54 ounces</font> of solution A
<font color=red>36 ounces</font> of solution B


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Work Shown


Method 1


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 = <font color=red>54</font>
B = 90-A = 90-54 = <font color=red>36</font>


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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 = <font color=red>36</font>
3x = 3*18 = <font color=red>54</font>
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.
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