Answer :
Using a system of equations, mix 3 oz of 15% moisturizer and 9 oz of 23% moisturizer to get 12 oz moisturizer that is 21% moisturizer.
How the mixture is determined using a system of equations:
The problem is asking to mix two types of face creams, one with 15% moisturizer and the other with 23% moisturizer, to get a 12 oz mixture that is 21% moisturizer.
Let the amount of the 15% cream = x
Let the amount of the 23% cream = y
We have two equations based on the problem:
The total amount of the mixture is 12 oz:
x + y = 12
The total amount of moisturizer is 21% of the total mixture:
0.15x + 0.23y = 0.21×12
=
0.15x + 0.23y = 2.52
Equation 1: x + y = 12
Equation 2: 0.15x + 0.23y = 2.52
Multiply Equation 1 by 0.15:
0.15x + 0.15y = 1.8 ...Equation 3
Subtract Equation 3 from Equation 2:
0.15x + 0.23y = 2.52
-
0.15x + 0.15y = 1.8
0.08y = 0.72
y = 9
Substitute y = 9 in Equation 2:
0.15x + 0.15y = 1.8
0.15x + 0.15(9) = 1.8
0.15x + 1.35 = 1.8
0.15x = 0.45
x = 3
