Explanation:
Let X be the number of pounds of peanuts selling for 85 cents per pound and Y be the number of pounds of peanuts selling for 98 cents per pound.
We can set up the following system of equations to represent this situation:
X * 0.85 + Y * 0.98 = 0.90 * (X + Y)
X + Y = 40
The first equation represents the total cost of the blend, and the second equation represents the total number of pounds of peanuts.
To solve this system of equations, we can use a method such as graphing, substitution, or elimination.
Using the substitution method, we can solve for one variable in terms of the other and substitute it into the other equation. For example, we can solve the first equation for X:
X = (0.90 * (X + Y) - Y * 0.98) / 0.85
Then, we can substitute this expression for X into the second equation:
(0.90 * (X + Y) - Y * 0.98) / 0.85 + Y = 40
Solving this equation for Y gives us the number of pounds of peanuts selling for 98 cents per pound:
Y = (40 * 0.85 - 0.90 * X) / (0.10 - 0.98)
To find the value of X, we can substitute this expression for Y into the first equation and solve for X:
X * 0.85 + (40 * 0.85 - 0.90 * X) / (0.10 - 0.98) * 0.98 = 0.90 * (X + (40 * 0.85 - 0.90 * X) / (0.10 - 0.98))
Solving this equation for X gives us the number of pounds of peanuts selling for 85 cents per pound:
X = 18.75
Therefore, 18.75 pounds of peanuts selling for 85 cents per pound must be mixed with 40 pounds of peanuts selling for 98 cents per pound to produce a blend selling for 90 cents per pound.