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?

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Mathematics

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17 June, 17:57

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?

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Answers (1)

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Judith Hess · 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