Nature's best wants to combine nuts they sell for $3.60 a pound with dried fruit they sell for $2.40 a pound to create a trail mix. How much of each snack should they use to make 10 pounds of trail mix that would sell for $3.30 a pound? Thank you!
To solve this problem, we can use a system of equations. Let's assume that 'x' represents the number of pounds of nuts and 'y' represents the number of pounds of dried fruit in the trail mix.
According to the given information, the nuts cost $3.60 per pound, the dried fruit costs $2.40 per pound, and the final trail mix should sell for $3.30 per pound. We also know that the total weight of the trail mix is 10 pounds.
Now, we can set up the following equations:
Equation 1: x + y = 10 (since the total weight is 10 pounds)
Equation 2: (3.60x + 2.40y) / 10 = 3.30 (since the average price of the trail mix is $3.30 per pound)
To solve these equations, we can use substitution or elimination method. Here, we'll use the elimination method.
First, multiply both sides of Equation 2 by 10 to eliminate the denominator:
3.60x + 2.40y = 33
Now, multiply Equation 1 by 2.40 to match the coefficients of 'y':
2.40x + 2.40y = 24
Subtract Equation 2 from Equation 1:
(2.40x + 2.40y) - (3.60x + 2.40y) = 24 - 33
-1.20x = -9
x = 9 / 1.20
x = 7.5
Substitute the value of 'x' back into Equation 1:
7.5 + y = 10
y = 10 - 7.5
y = 2.5
Therefore, Nature's Best should use 7.5 pounds of nuts and 2.5 pounds of dried fruit to make 10 pounds of trail mix that would sell for $3.30 per pound.