Pre calc question

Question

A chemist needs to create a 65% HCl solution. (HCl is hydrochloric acid. A "65% HCl solution" contains 65% HCl and the other 35% is water.)

How much of a 87.5% HCl solution must be mixed with 20 ml of a 45% HCl solution in order to result in a 65% HCl solution?

Round your answer to 2 places after the decimal point (if necessary) and do NOT type any units (such as "ml") in the answer box.

Amount of 87.5% HCl solution:

Answer 1

Let "x" be the amount of 87.5% solution. That means, after you mix in 20 mL of 45% solution, you will have a total of "x + 20" mL.

So:

0.875x + 0.45(20) = 0.65(x + 20)

0.875x + 9 = 0.65x + 13

0.225x = 4

x = 160/9 or approx 17.8 mL of 87.5% HCl solution

Answer 2

Let x be the amount of the 87.5% solution to add to the 20 ml of 45% solution.

0.875x + 0.45(20) = 0.65(20+x)

0.875x+9 = 13+0.65x

0.225x = 4

x = 0.225/4 ≈ 17.78

Answer 3

Hi Fadi Tatar E

Let x = amount you need to add

20(.45) = the amount of HCl present in 20 ml

0.875x = the amount of 87.5% HCl in x the amount you need to add

((20(.45)+.875x)/20 + x = .65

20(.45)+.875x = .65(20 + x)

Solving for x

x = 17.78

Checking

[(20*.45) + .875(17.78)/(20 + 17.78)]*100

[9 + 15.56/37.78] *100 = 24.56/37.78 *100= 65%

Hope this helps please write if you have any questions.