Tom needs to make 75 ml of a 40% alcohol solution. He is going to make it by mixing a 50% alcohol solution with a 5% alcohol solution. How much of each should he use?

Question

Tom needs to make 75 ml of a 40% alcohol solution. He is going to make it by mixing a 50% alcohol solution with a 5% alcohol solution. How much of each should he use?

Answer 1

75(40) = x(50) + (75-x)5

3000 = 50x +375-5x

45x =3000-375 = 2625

x = 2625/45 = 58 1/3 ml of 50%

(75-x) = 16 2/3 ml of 5%

50 is much closer to 40 than 5 is, so you know you need much more of 50% than 5% to get a mixture of 40%

40 is within 10 of 50 and within 35 of 5

35/10 = 3 1/2. You'll need 3 1/2 times as much 50% as 5%.

58 1/3 is 3.5 times 16 2/3. (3 1/2)(16 2/3) = 7/2(50/3) = 7(25)/3 = 175/3 = 58 1/3