A chemical manufacturer wishes to fill an order for 700 gallons of a 24% acid solution. Solutions of 20% and 30% are in stock.

How many gallons of 20% acid solution will be used in the desired mixture?

x = 420

To find out how many gallons of 20% acid solution will be used in the desired mixture, we need to set up an equation.

Let x represent the number of gallons of the 20% acid solution.

The 20% acid solution contains 20% acid, so the amount of acid in these x gallons will be 0.2x.

Since we need a total of 700 gallons of the final mixture, the amount of 30% acid solution used will be 700 - x.

The 30% acid solution contains 30% acid, so the amount of acid in these 700 - x gallons will be 0.3(700 - x).

To obtain a 24% acid solution, the total amount of acid in the mixture should be 24% of the 700 gallons:

0.2x + 0.3(700 - x) = 0.24(700)

Now, we can solve this equation to find x:

0.2x + 210 - 0.3x = 168

-0.1x = -42

x = -42 / -0.1

x = 420

So, 420 gallons of the 20% acid solution will be used in the desired mixture.

To determine how many gallons of 20% acid solution will be used in the desired mixture, we can set up an equation based on the information given.

Let's assume x gallons of 20% acid solution will be used.

The acid content in the 20% acid solution will be 0.20x gallons.

Similarly, the acid content in the 30% acid solution will be 0.30(700 - x) gallons, since the total order is 700 gallons and we are using x gallons of the 20% solution.

The total acid content in the desired mixture should be 0.24(700) gallons, which can be expressed as 168 gallons.

Therefore, the equation becomes:

0.20x + 0.30(700 - x) = 168

Simplifying the equation, we get:

0.20x + 210 - 0.30x = 168

Combining like terms, we have:

-0.10x = -42

Dividing both sides by -0.10, we find:

x = 420

Hence, 420 gallons of the 20% acid solution will be used in the desired mixture.

amount of the 20% stuff ---- x gallons

amount of the other stuff ---- 700-x

.2x +.3(700-x) = .24(700)

solve for x to reveal the mystery.