Answer:
12 pounds of the $0.95/lb candy and 15 pounds of the $1.85/lb
Explanation:
To solve this math problem step by step, we can use a system of equations to represent the given information and find the values for the unknown variables. Let's break it down:
1. Assign variables: Let's assign variables to the unknowns in the problem. Let's say x represents the pounds of candy worth $0.95/lb, and y represents the pounds of candy worth $1.85/lb.
2. Set up equations: We can set up two equations based on the given information. The first equation represents the total weight of the mixture, and the second equation represents the total value of the mixture.
Equation 1: x + y = 27 (since the total weight of the mixture is 27 lb)
Equation 2: (0.95x) + (1.85y) = 1.45(27) (since the total value of the mixture is $1.45/lb multiplied by 27 lb)
3. Solve the system of equations: We can solve the system of equations using various methods such as substitution or elimination. Let's use the substitution method here.
From Equation 1, we can express x in terms of y: x = 27 - y.
Substituting this value of x into Equation 2, we get:
(0.95(27 - y)) + (1.85y) = 1.45(27)
Simplifying the equation:
25.65 - 0.95y + 1.85y = 39.15
Combining like terms:
0.9y = 13.5
Dividing both sides by 0.9:
y = 15
4. Find the value of x: Now that we have the value of y, we can substitute it back into Equation 1 to find x:
x + 15 = 27
x = 27 - 15
x = 12
5. Interpret the results: The solution to the system of equations tells us that 12 pounds of candy worth $0.95/lb and 15 pounds of candy worth $1.85/lb were used to make a 27-pound mixture.
Therefore, 12 pounds of the $0.95/lb candy and 15 pounds of the $1.85/lb candy were used to make the 27 lb mixture.