Question

Solve the following problem using linear systems: You have a bottle of a 2% solution of iodine and a bottle of a 66% solution of iodine. You need 16 liters of a 47% solution. How many liters of the 2% and 66% solutions should you mix together?

Answer 1

The quantity of liters of the 2% and 66% solutions should you mix together is 4.75 and 11.25 liters.

let

• x = liters of 2% solution
• y = liters of 66% solution

x + y = 16

0.02x + 0.66y = 0.47 × 16

from (1)

x = 16 - y

Substitute into (2)

0.02x + 0.66y = 0.47 × 16

0.02(16 - y) + 0.66y = 7.52

0.32 - 0.02y + 0.66y = 7.52

- 0.02y + 0.66y = 7.52 - 0.32

0.64y = 7.20

y = 7.20/0.64

y = 11.25 liters

Substitute y = 11.25 liters into (1)

x + y = 16

x + 11.25 = 16

x = 16 - 11.25

x = 4.75 liters

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