How many pounds of mixed nuts selling for $4.50 a pound should be mixed with 20 lbs of dried fruit selling for $5.50 a pound to obtain a trail mix that sells for $5 a pound?
4.50x + 5.50*20 = 5.00(x+20)
To find out how many pounds of mixed nuts you should mix with the dried fruit, let's break down the problem step by step:
Let x represent the number of pounds of mixed nuts to be mixed.
Now, let's look at the cost of the components:
The cost of the mixed nuts per pound is $4.50.
The cost of the dried fruit per pound is $5.50.
The desired cost of the trail mix per pound is $5.00.
Next, let's calculate the cost of the components:
The total cost of the mixed nuts will be x pounds multiplied by $4.50 per pound, so it will be 4.50x dollars.
The total cost of the dried fruit will be 20 pounds multiplied by $5.50 per pound, so it will be 110 dollars.
Now, let's calculate the total cost of the trail mix:
The total cost of the trail mix will be the sum of the cost of the mixed nuts and the cost of the dried fruit. Therefore, it will be 4.50x + 110 dollars.
Since the desired cost of the trail mix is $5.00 per pound, we can set up the equation:
5.00 = (4.50x + 110) / (x + 20)
Let's solve this equation to find the value of x:
Multiply both sides of the equation by (x + 20) to remove the denominator:
5.00(x + 20) = 4.50x + 110
Expand the multiplication:
5.00x + 100 = 4.50x + 110
Subtract 4.50x from both sides of the equation:
0.50x + 100 = 110
Subtract 100 from both sides of the equation:
0.50x = 10
Divide both sides of the equation by 0.50 to isolate x:
x = 10 / 0.50
Simplify the right side of the equation:
x = 20
Therefore, you should mix 20 pounds of mixed nuts with the dried fruit to obtain a trail mix that sells for $5.00 a pound.