A scientist has two solutions which she has labeled solution A and solution B. Each contains salt. She knows that solution A is 30% salt and solution B is 55% salt. She wants to obtain 60 ounces of mixture that is 45% salt. How many ounces of each solution should she use?

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jitushashi120 jitushashi120 · Answer 1 · 2019-12-09T08:54:45+01:00

Answer:

A= 24 ounces and B= 36 ounces.

Step-by-step explanation:

Given: Solution A contain 30% salt= 0.30 salt.

Solution B contain 55% salt= 0.55 salt.

New mixture should be of 60 ounces with 45% salt.

Let x be the amount of mixture for solution A. Let y be the amount of mixture of solution B.

Scientist need to to obtain 60 ounce of mixture from solution A and B.

∴ [tex]x+y= 60\ ounces[/tex]

y= [tex]60-x[/tex] equation 1

Now, solving to get final solution.

∴ [tex]0.3x+0.55y=0.45\times 60\ ounces[/tex]

Substituting the value of y from equation 1

⇒ [tex]0.3x+ 0.55\times (60-x)= 27[/tex]

⇒ [tex]0.3x+33-0.55x= 27[/tex]

⇒ [tex]-0.25x= -6[/tex]

∴ x= 24 ounces

Next, finding y

y= 60-x

∴ y= [tex]60-24= 36\ ounces.[/tex]

y= 36 ounces.

Now, we can say scientist would require 24 ounces of solution A and 36 ounces of solution B to obtain mixture of 60 ounces with 45% salt.