a chemist needs to prepare 28 ounces of a 8% hydrochloric acid solution. find the amount of 14% solution and the amount of 7% solution he should mix to get this solution.
amount of 14% solution --- x
amount of 6% solution ----- 28-x
solve for x:
.14x + .07(28-x) = .08(28)
I suggest multiplying each term by 100 to get rid of those pesky decimals
To find the amounts of 14% and 7% solutions that need to be mixed to prepare 28 ounces of an 8% hydrochloric acid solution, we need to set up an equation.
Let x represent the amount of the 14% solution in ounces, and (28 - x) represent the amount of the 7% solution in ounces.
The equation can be set up as follows:
0.14x + 0.07(28 - x) = 0.08(28)
Here's a step-by-step solution of the equation:
1. Multiply the percentages by the respective amounts:
0.14x + 0.07(28 - x) = 0.08(28)
2. Distribute the terms:
0.14x + 1.96 - 0.07x = 2.24
3. Combine like terms:
0.07x + 1.96 = 2.24
4. Subtract 1.96 from both sides:
0.07x = 0.28
5. Divide both sides by 0.07 to isolate x:
x = 4
Therefore, the chemist needs to mix 4 ounces of the 14% solution and (28 - 4) = 24 ounces of the 7% solution to prepare 28 ounces of an 8% hydrochloric acid solution.