Anew 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 $3 per ounce. if the new self-tanning & moisturizing lotion mixture is to cost $ 1.60 per ounce, how many ounces of the self-tanning lotion should be in the mixture?

450 ounces

Step-by-step explanation:

We know that the cost of the mixture must be the cost of the everyday moisturizing lotion plus the cost of the self-tanning lotion , which means .

The cost of any substance will be the cost per ounce of the substance (c), multiplied by the number of ounces (n), which means C=nc, so we have from the previous formula that we have:

But we also know that the number of ounces of the mixture must be the sum of the number of ounces of the everyday moisturizing lotion with the number of ounces of the self-tanning lotion, so we have

We want to calculate the number of ounces of the self-tanning lotion (), so we solve for that variable:

And substitute our values in this formula, to get: