To begin, let's assume that the perfume is made up of x ounces of 15% scented Thalia and y ounces of 40% scented Thalia.
According to the problem, the total amount of perfume is 60 oz, so we have:
x + y = 60 ----(1)
We also know that the desired strength of Thalia in the perfume is 25%, so the amount of Thalia in the perfume should be 0.25 * 60 = 15 oz.
The amount of Thalia in x ounces of 15% scented Thalia is 0.15x, and the amount of Thalia in y ounces of 40% scented Thalia is 0.40y.
Therefore, we have the equation:
0.15x + 0.40y = 15 ----(2)
Now, we can solve equations (1) and (2) simultaneously to find the values of x and y.
Multiplying equation (1) by 0.15 and subtracting it from equation (2) multiplied by 0.40, we get:
0.40y - 0.15x = 15 - 0.15 * 60
0.40y - 0.15x = 15 - 9
0.40y - 0.15x = 6 ----(3)
Now, we can solve equations (1) and (3) simultaneously to find the values of x and y.
Multiplying equation (1) by 0.15 and equation (3) by -1, we get:
0.15x - 0.15y = 0
-0.15x + 0.40y = -6
Adding the two equations together, we have:
0.15x - 0.15x + 0.40y + 0.15y = 0 - 6
0.55y = -6
y = -6 / 0.55
y ≈ -10.909
Since we can't have a negative amount of perfume, it means the assumption is incorrect. The problem as formulated has no solution.
Perfumes are made using different concentrations of scents to create unique fragrances. Suppose perfume is made from t ounces of 15% scented Thalia and b ounces of 40% Thalia. You want to make 60 oz. of a perfume that has 25% blend of Thalia.
How many ounces of each concentration of Thalia are needed to get 60 oz. of perfume that is 25% strength Thalia?
1 answer
1 answer