Question

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 35% salt and Solution B is 60% salt. She wants to obtain 150 ounces of a mixture that is 45% salt. How many ounces of each solution should she use?

Answer 1

Answers:

90 ounces of solution A.

60 ounces of solution B.

====================================================

Step-by-step explanation:

x = amount of solution A

150-x = amount of solution B

Each amount is in ounces and they add to 150 ounces.

Solution A is 35% salt, so we get 0.35x ounces of pure salt from solution A.

Solution B is 60% salt, so we get 0.60*(150-x) = 90-0.60x ounces of pure salt from solution B.

We want 150 ounces of 45% salt solution, which means we want 150*0.45 = 67.5 ounces of pure salt when everything is mixed.

Here's a table showing this info

`\begin{array} \cline{1-3}& \text{Mixture} & \text{Pure Salt}\\\cline{1-3}\text{Solution A} & \text{x} & 0.35\text{x}\\\cline{1-3}\text{Solution B} & 150-\text{x} & 0.60(150-\text{x}) = 90-0.60\text{x}\\\cline{1-3}\text{Total} & 150 & 150*0.45 = 67.5 \\\cline{1-3}\end{array}`

Cleaning up the table a bit shows

`\begin{array}c \cline{1-3}& \text{Mixture} & \text{Pure Salt}\\\cline{1-3}\text{Solution A} & \text{x} & 0.35\text{x}\\\cline{1-3}\text{Solution B} & 150-\text{x} & 90-0.60\text{x}\\\cline{1-3}\text{Total} & 150 & 67.5 \\\cline{1-3}\end{array}`

Focus on the "pure salt" column.

We want the 0.35x and 90-0.60x to add to 67.5

So,

0.35x+(90-0.60x) = 67.5

90-0.25x = 67.5

-0.25x = 67.5-90

-0.25x = -22.5

x = -22.5/(-0.25)

x = 90

She must use 90 ounces of solution A.

150-x = 150-90 = 60 ounces of solution B must be used as well.

-------------------

Check:

35% of 90 = 0.35*90 = 31.5 ounces of pure salt comes from solution A.

60% of 60 = 0.60*60 = 36 ounces of pure salt comes from solution B.

31.5+36 = 67.5 ounces of pure salt in total, which matches with the value mentioned earlier. The answers are confirmed.