Question

A drugoist has two mixtures of a certain chemical and water, one containing 10% of the chemical and the other

containing 40% of the chemical. How much of each mixture should he use to make 10 ounces that contain 25% of the
chemical?
05
25

Answer 1

5 ounces of each chemical

Explanation:

Let 'x' ounces of 10% chemical be mixed to the solution.

Given:

Ounces of 10% chemical = 'x'

Total ounces in the solution to make = 10

Therefore, the ounces of 40% chemical =
`10 - x`

Now, Content of chemical in the first mixture =
`10\%\ of\ x = 0.1x`

Content of chemical in the second mixture =
`40\%\ of\ (10-x) = 0.4(10-x)`

Now, total volume of the chemical in the solution is 25% of 10 = 0.25(10). So,

Total volume = Volume of chemical in first mixture + second mixture

`0.25(10)=0.1x+0.4(10-x)\\\\2.5=0.1x+4-0.4x\\\\2.5-4=-0.3x\\\\-1.5=-0.3x\\\\x=(-1.5)/(-0.3)=5\ oz`

Therefore, volume of 10% chemical is
`x=5\ oz`

Volume of 40% chemical is
`10-x=10-5=5\ oz`

Hence, 5 ounces of each chemical is needed to make 10 ounces of solution.