Answer: You need 2 pounds of peanuts costing $1.75/lb mixed with 1 pound of raisins costing $2.50/lb to make 3 pounds of a mixture that costs $2.00/lb.
Explanation:
Let's solve this problem step by step:
Let x represent the number of pounds of peanuts (costing $1.75/lb) needed.
Calculate the cost of the peanuts: x pounds * $1.75/pound = $1.75x.
Calculate the cost of raisins: Since you have 3 pounds of the mixture and it costs $2.00/lb, the total cost of the mixture is 3 pounds * $2.00/lb = $6.00.
Now, we need to find out how many pounds of raisins (costing $2.50/lb) are in the mixture. Let y represent the number of pounds of raisins.
Calculate the cost of raisins: y pounds * $2.50/pound = $2.50y.
Since the total cost of the mixture is $6.00, we can set up the equation:
$1.75x + $2.50y = $6.00
We also know that the total weight of the mixture is 3 pounds:
x + y = 3
Now, you have a system of two equations with two variables:
$1.75x + $2.50y = $6.00
x + y = 3
We can solve this system of equations to find the values of x (pounds of peanuts) and y (pounds of raisins) needed.
Let's start by solving equation 2 for x:
x = 3 - y
Now, substitute this expression for x into equation 1:
$1.75(3 - y) + $2.50y = $6.00
Now, distribute the $1.75 on the left side of the equation:
$5.25 - $1.75y + $2.50y = $6.00
Combine like terms:
$0.75y = $6.00 - $5.25
$0.75y = $0.75
Now, divide by $0.75 to solve for y:
y = 1
Now that you know the number of pounds of raisins needed (y = 1 pound), you can find the number of pounds of peanuts (x):
x = 3 - y
x = 3 - 1
x = 2
So, you need 2 pounds of peanuts costing $1.75/lb mixed with 1 pound of raisins costing $2.50/lb to make 3 pounds of a mixture that costs $2.00/lb.