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?
Accepted Solution
A:
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 1Now, 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 ouncesNext, 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.