Determine the number of pounds of nuts selling for $6 per pound and raisins selling for $3 per pound
that should be combined to create 60 pounds of a trail mix selling for $5 per pound.
Determine the number of pounds of nuts selling for $6 per pound and raisins selling for $3 per pound
that should be combined to create 60 pounds of a trail mix selling for $5 per pound.
To solve this problem, we can set up a system of equations.
Let's denote the number of pounds of nuts as 'x' and the number of pounds of raisins as 'y'.
According to the problem, we need to create a total of 60 pounds of trail mix. Therefore, our first equation is:
x + y = 60
Next, we need to consider the costs. The nuts sell for $6 per pound, so the total cost of the nuts is 6x. The raisins sell for $3 per pound, so the total cost of the raisins is 3y. To create the trail mix, which sells for $5 per pound, the total cost of the nuts and raisins combined should be 5 times the total weight of the trail mix, which is 60 pounds. Therefore, our second equation is:
6x + 3y = 5 * 60
So, our system of equations is:
x + y = 60
6x + 3y = 300
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve by the method of substitution:
From the first equation, we can express x in terms of y:
x = 60 - y
Substituting this value of x into the second equation, we get:
6(60 - y) + 3y = 300
360 - 6y + 3y = 300
-3y = 300 - 360
-3y = -60
y = -60 / -3
y = 20
Now that we have the value of y, we can substitute it back into the first equation to find x:
x + 20 = 60
x = 60 - 20
x = 40
Therefore, to create 60 pounds of trail mix, we need 40 pounds of nuts and 20 pounds of raisins.