Question

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?

Answer 1

A= 24 ounces and B= 36 ounces.

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.

∴
`x+y= 60\ ounces`

y=
`60-x` equation 1

Now, solving to get final solution.

∴
`0.3x+0.55y=0.45* 60\ ounces`

Substituting the value of y from equation 1

⇒
`0.3x+ 0.55* (60-x)= 27`

⇒
`0.3x+33-0.55x= 27`

⇒
`-0.25x= -6`

∴ x= 24 ounces

Next, finding y

y= 60-x

∴ y=
`60-24= 36\ ounces.`

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.