How many ounces of a 13% solution and a 42% solution must be combined to obtain 58 ounces of a 15% solution?

Question

Need to know how many ounces of the 13% solution and how many ounces of the 42% solution separately. This is one part of the assignment that my online class did not go over. Thanks!

Answer 1

You can use alligation or algebra.

Alligation:

HAVE...............WANT............USE

13%........................................27 PARTS

............................15%............................

42............................................2 PARTS

So 29 parts = 58 ounces and each part thus equals = 2 ounces

Use 2 x 27 = 54 ounces of 13% and 2 x 2 = 4 ounces of 42%

Algebra:

(x)(13%) + (58-x)(42%) = (58)(15%)

13x + 2436 - 42x = 870

-29x = -1566

x = 54 ounces of 13% and

4 ounces of 42%

Answer 2

Let x and y be the weights of the two solutions before combining

x+y = 58 --> y = 58-x

0.13x +0.42y = 0.15(58)

0.13x + 0.42(58-x) = 8.7

0.13x + 24.36 - 0.42x = 8.7

0.29x = 15.66

x = 15.66/0.29 = 54

y = 58-54 = 4

54 ounces of the 13% solution plus 4 ounces of the 42% solution.