Answer:
Number of ounces of 28% alcohol = x = 34 ounces
Number of ounces of 40% alcohol = y = 17 ounces
Step-by-step explanation:
Let us represent the
Number of ounces of 28% alcohol = x
Number of ounces of 40% alcohol = y
Our system of equations =
x + y = 51 ..... Equation 1
x = 51 - y
28% × x + 40% × y = 32% × 51
0.28x + 0.4y = 16.32......Equation 2
We substitute 51 - y for x
0.28(51 - y) + 0.4y = 16.32
14.28 - 0.28y + 0.4y = 16.32
- 0.28y + 0.4y = 16.32 - 14.28
0.12y = 2.04
y = 2.04/0.12
y = 17
Solving for x
x = 51 - y
x = 51 - 17
x = 34
Therefore,
Number of ounces of 28% alcohol = x = 34 ounces
Number of ounces of 40% alcohol = y = 17 ounces
