Kristen wants to make 45 ounces of a 50 jasmine essential oi

Kristen wants to make 4.5 ounces of a 50% jasmine essential oil. She only has a 30% jasmine mixture and a 60% jasmine mixture available. How much of each mixture should she combine to create the desired oil?

Kristen should use _ ounce(s) of the 30% mixture and _ ounce(s) of the 60% mixture.

Solution

Let x = number of ounces of 30% mixture and

y = number of 60% mixture.

Then x + y = 4.5

Subtracting x from both the sides,

y = 4.5 - x...(1)

Also,

0.3x + 0.6y = 0.5 (x+y)

0.3x + 0.6(4.5-x) = 0.5 (x + 4.5 -x)

0.3x + 2.7 - 0.6x = 0.5(4.5)

-0.3x + 2.7 = 2.25

Subtracting 27 from both the sides,

-0.3x = -0.45

Dividing both sides by -0.3,

x = 1.5

Substitute this in (1), y = 4.5 -1.5 = 3

So x=1.5 and y = 3