Question

A new mixture of​ self-tanning & moisturizing lotions for everyday use is being developed. This mixture is made by mixing 700 ounces of everyday moisturizing lotion for ​$0.70 per ounce with​ self-tanning lotion worth ​$22 per ounce. If the new​ self-tanning & moisturizing lotion mixture is to cost $ 1.30 per​ ounce, how many ounces of the​ self-tanning lotion should be in the​ mixture?

Answer 1

For each ounce of the product, let
x = ounces of moisturizing lotion used,
y = ounces of self-tanning lotion used.

The sum of the two lotions per ounce is equal to one ounce. Therefore
x + y = 1 (1)

Moisturizing lotion costs $0.70 per ounce.
Self-tanning lotion costs $22 per ounce.

Because the product costs $1.30 per ounce. Therefore
0.70x + 22y = 1.30 (2)

From (1), obtain
y = 1 - x (3)

Substitute (3) into (2).
0.70x + 22(1 - x) = 1.30
0.70x - 22x + 22 = 1.30
-21.3x = -20.7
x = 0.9718 ounces
From (3), obtain
y = 1 - 0.9718 = 0.0282 ounces.

A batch of the product is 700 ounces. Therefore the amount of self-tanning lotion used is
700*y = 700*0.0282 = 19.74 ounces

Answer: 19.74 ounces