Answer:
She combines 9.3 kg of each.
Step-by-step explanation:
Let x = amount of brand A in kg
Let y = amount of peanuts in kg
First we deal with the amount of each product she uses.
"Ashley sells 18.6 kg bags of mixed nuts that contain 60% peanuts."
x + y = 18.6
Now we deal with just the amount of peanuts.
"To make her product she adds peanuts to Brand A's mixed nuts which contain 20% peanuts."
Brand A contains 20% peanuts, so x kg of brand A contains 0.2x kg of peanuts.
The peanuts she adds are pure peanuts, so all of y is peanuts.
The result is 18.6 kg of a mixture that is 60% peanuts, so the amount of peanuts in the bags she sells is 0.6 * 18.6 kg.
0.2x + y = 0.6 * 18.6
0.2x + y = 11.16
We have a system of equations:
x + y = 18.6
0.2x + y = 11.16
We have y in both equations, so let's subtract the second equation from the first equation to eliminate y.
0.8x = 7.44
Divide both sides by 0.8
x = 9.3
Plug in 9.3 for x in the first equation of the system and solve for y.
x + y = 18.6
9.3 + y = 18.6
y = 9.3
Answer: She combines 9.3 kg of each.
