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.