Question

a scientist has two solutions which she has labeled solution a and solution b. each contains salt. She knows that solution A is 30% salt and solution b is 55% salt. She wants to obatin 150 ounces of a mixture that is 40% sal. How many ounces of eahc solution should she use

Answer 1

a = 90 ounce

b = 60 ounce

Explanation:

Let:

a = total ounce of solution a

b = total ounce of solution b

a mixture that is 40% salt → salt = 40% × 150 = 60 ounce

She wants to obtain 150 ounces of a mixture → a + b = 150 ... [1]

salt = 60 ounce → 30%(a) + 55%(b) = 60

0.3a + 0.55b = 60

30a + 55b = 6000

6a + 11b = 1200 ... [2]

[1] + [2]

a + b = 150 | x6 | ⇔ 6a + 6b = 900

6a + 11b = 1200 | x1 | ⇔ 6a + 11b = 1200

------------------------------- (-)

-5b = -300

b = 60

[1]

a + b = 150

a + 60 = 150

a = 90