Answer:
To make 7 pounds of trail mix that costs $6 per pound:
You need 2.8 pounds of granola.
You need 4.2 pounds of assorted nuts.
Explanation:
Let's call the number of pounds of granola G and the number of pounds of assorted nuts N that are needed to make 7 pounds of trail mix that costs $6 per pound.
The total cost of the trail mix is $6 per pound times 7 pounds, which is $42.
Now, we can set up a system of equations based on the cost of the granola and nuts:
The cost of the granola (G pounds) is $4.50 per pound, so it is 4.50G dollars.
The cost of the assorted nuts (N pounds) is $7 per pound, so it is 7N dollars.
We know that the total cost should be $42:
4.50G + 7N = 42
Now, we need to find a combination of G and N that satisfies this equation and also adds up to a total of 7 pounds:
G + N = 7
We have a system of two equations with two variables:
4.50G + 7N = 42
G + N = 7
We can solve this system of equations simultaneously. Let's solve for G and N:
First, let's solve equation 2 for G:
G = 7 - N
Now, substitute this expression for G into equation 1:
4.50(7 - N) + 7N = 42
Expand and solve for N:
31.50 - 4.50N + 7N = 42
Combine like terms:
2.50N = 42 - 31.50
2.50N = 10.50
Now, divide both sides by 2.50 to find N:
N = 10.50 / 2.50
N = 4.2
So, you would need 4.2 pounds of assorted nuts.
Now, use the value of N to find G from equation 2:
G = 7 - N
G = 7 - 4.2
G = 2.8
You would need 2.8 pounds of granola.
To make 7 pounds of trail mix at $6 per pound, you would need 2.8 pounds of granola and 4.2 pounds of assorted nuts.