A perfume maker wishes to blend perfume valued at $ 410 an ounce with perfume worth $ 250 an ounce to obtain a mixture of 40 ounce worth $ 300 an ounce. How much of the $ 410 perfume should he use?
If you take the amount of $410 perfume to be used as x ounces, the amount of $250 perfume to be used becomes (40-x) ounces.
For the final mixture to be worth $300 an ounce:
410x + 250(40-x) = 300(40)
Solve for x
To solve this problem, we can use the method of mixtures.
Let's assume the amount of perfume valued at $410 per ounce that the perfume maker wants to use is x ounces. Thus, the amount of perfume worth $250 per ounce would be (40 - x) ounces.
The value of the mixture can be calculated by multiplying the amount of each perfume blend with its value per ounce:
Value of $410 perfume = x * $410
Value of $250 perfume = (40 - x) * $250
Since the mixture is worth $300 per ounce, the equation can be set up as follows:
($410 * x) + ($250 * (40 - x)) = (40 * $300)
Simplifying the equation:
410x + (250 * 40) - (250 * x) = 12000
410x + 10000 - 250x = 12000
410x - 250x = 12000 - 10000
160x = 2000
x = 2000 / 160
x = 12.5
Therefore, the perfume maker should use 12.5 ounces of the perfume valued at $410 per ounce to obtain the desired mixture.