How do I solve this in steps?

Question

You need a 70% alcohol solution. On hand, you have a 80 mL of a 5% alcohol mixture. You also have 80% alcohol mixture. How much of the 80% mixture will you need to add to obtain the desired solution?

Answer 1

5(80) + 80(x) = 70(80+x), solve for x. x= how much of the 80% you need to get 70% mixture

80 ml of 5% + x ml of 80% gives 80+x ml of 70%

400 + 80x = 5600 + 70x

80x - 70x = 5600-400

10x = 5200

x = 520 ml of 80% solution needed to get a mixture of 70% solution

You're trying to get 80% from 70% and 5%. 80 is much closer to 70 than to 5, so you know you'll need far more of the 70 than of the 5 solution. 520/80 is the ratio of 80 to 5 = 52/8 = 6.5/1

70 is within 10 of 80, 70 is within 65 of 5. that's a ratio of 65/10 = 6.5/1. You need 6 1/2 times as much 80% solution as you have 5% solution. 6 1/2 times 80 = 520 ml.