You would do best making a table with this info. The 3 rows would be 20% HCl, 70% HCl, and mix. The 3 columns would be number of ounces, %HCl, and total. The formula has us multiplying the number of ounces times the % HCl to equal the total. In the first row first column you are going to enter "x" because you don't know how much 20% HCl you have, in the %HCl you are going to enter .20 because that' the decimal equivalent to 20%, and in the last column you are going to put the product of x and .2 which is .2x. In the second row first column you are going to put a y, since you don't know how much 70% HCl you have, in the second row second column under %HCl you are going to enter .7 since that's the decimal equivalent to 70%, and the last column has you multiplying the y and the ,7 to get .7y. Now for the third row first column you are going to enter 20 since your mix of the 2 strengths of acids is going to yield 20 ounces. Third row second column is going to be .5 since you are looking to make a mixture that is 50% HCl and .5 is the decimal equivalent to 50%. The third row third column is the product of 20 and .5 which is 10. Now that you table is full...you are adding the number of ounces of strengths of acids to make 20 ounces, so the first equation you get from this table is x + y = 20. The last column, the total column is also added because those are the percent strength of each one combined to equal the product 10. Number of ounces and percent strengths are different so that's why we have 2 equations. A system, in other words. .20x + .7y = 10. That's the second equation. Solve the first one for x. x = 20 - y. Sub that value in for x in the second equation to get .20(20 - y) + .7y = 10. Distributin gives us 4-.2y+.7y = 10. Combining like terms leaves us with .5y = 6 and y = 12. That means that there is 12 ounces of 70%HCl. Solving for the amount of 20% HCl is 20 - 12 = 8. There is 8 ounces of 20% HCl, since 12 + 8 = 20 ounces.
Answer:
8 ounces of 20%12 ounces of 70%
Step-by-step explanation:
Let 'x' be the number of ounces of 20% solution'y' be for the 70% solutionSince the the mix is 50% of 20 ounces then:x + y = 200.20x + 0.70y = 0.50(20)From the 1st equation solve for xx = 20 - ySubstitute it to the 2nd equation0.2(20-y) + 0.7y = 104 - 0.2y + 0.7y = 100.5y = 10-40.5y = 6y = 12Substitute to x = 20 - yx = 20 - 12x = 8
