Question

A scientist has two solutions, which she had labeled solution A and solution B. each contains salt. she knows that solution A is 65% salt and Solution B is 90% salt. She wants to obtain 40 ounces of a mixture that is 85% salt. How many ounces of each solution should she use?

Answer 1

`A +B = 40` (1)

`A*0.65 + B*0.90 = 40*0.85` (2)

From equation (1) we can solve for A and we got:

`A = 40 -B` (3)

And replacing equation (3) into equation (2) we got:

`(40-B)*0.65 +0.9 B =34`

And solving the last equation for B we got:

`26 -0.65 B +0.9 B= 34`

`B = (8)/(0.25)= 32`

And solving for A from equation (3) we got:

`A = 40-32 = 8`

So then we need 8 ounces of solution A with concentration of 65% of salt and 32 ounces of solution B with 90% of salt

Explanation:

Let A represent the amount of solution A and B the amount of solution B. We know that the concentration of A is 65% and the concentration for B is 90%.

We want to obtain a solution of 40 ounces with a concentration of 85% of salt.

Based on this we can set up the following equations:

`A +B = 40` (1)

`A*0.65 + B*0.90 = 40*0.85` (2)

From equation (1) we can solve for A and we got:

`A = 40 -B` (3)

And replacing equation (3) into equation (2) we got:

`(40-B)*0.65 +0.9 B =34`

And solving the last equation for B we got:

`26 -0.65 B +0.9 B= 34`

We subtract in both sides 36:

`0.25 B =8`

And dividing both sides by 0.25 we got:

`B = (8)/(0.25)= 32`

And solving for A from equation (3) we got:

`A = 40-32 = 8`

So then we need 8 ounces of solution A with concentration of 65% of salt and 32 ounces of solution B with 90% of salt