Final answer:
To make a 3-oz bottle of perfume sold for $63, 2.1 oz of Perfume A and 0.9 oz of Perfume B should be combined.
Step-by-step explanation:
To determine how much of each perfume should be combined to make a 3-oz bottle of perfume that can be sold for $63, we can set up a system of equations. Let's represent the amount of Perfume A in ounces as x, and the amount of Perfume B in ounces as y. We know that Perfume A sells for $15 per ounce and Perfume B sells for $35 per ounce. So, the total cost of Perfume A is 15x dollars and the total cost of Perfume B is 35y dollars. We also know that the total volume of the mixture is 3 oz and the total cost of the mixture is $63. From this information, we can set up the following system of equations:
- x + y = 3 (equation representing the total volume of the mixture)
- 15x + 35y = 63 (equation representing the total cost of the mixture)
To solve this system of equations, we can use the method of substitution or elimination. In this case, let's use substitution. Solve the first equation for x: x = 3 - y. Substitute this expression for x in the second equation: 15(3 - y) + 35y = 63. Simplify and solve for y: 45 - 15y + 35y = 63. Combine like terms: 45 + 20y = 63. Subtract 45 from both sides: 20y = 18. Divide by 20: y = 0.9. Substitute this value back into the first equation to solve for x: x + 0.9 = 3. Subtract 0.9 from both sides: x = 2.1. Therefore, 2.1 ounces of Perfume A and 0.9 ounces of Perfume B should be combined to make a 3-oz bottle of perfume that can be sold for $63.