Randall wants to mix 57 lbs of nuts worth $1 per lb with some nuts worth $6 per lb to make a mixture worth $5 per lb. how many lbs of $6 nuts must he use?
1*57 + 6*x = 5(57+x)
To solve this problem, we can use the concept of weighted averages.
Let's assume Randall needs to mix x pounds of $6 nuts with the 57 pounds of $1 nuts.
The total cost of the mixture is calculated by multiplying the weight of each type of nut by its respective cost per pound and then dividing by the total weight of the mixture. So, the equation for the total cost is:
(1 * 57 + 6 * x) / (57 + x) = 5
Now, we can solve this equation to find the value of x.
Multiplying both sides of the equation by (57 + x), we get:
1 * 57 + 6 * x = 5 * (57 + x)
57 + 6x = 285 + 5x
Subtracting 5x from both sides, we have:
x = 285 - 57
x = 228
Therefore, Randall needs to mix 228 pounds of $6 nuts to make the mixture worth $5 per pound.
To find the number of pounds of $6 nuts Randall must use, let's set up an equation.
Let x represent the number of pounds of $6 nuts.
The total weight of the mixture will be 57 lbs + x lbs.
The total cost of the mixture will be the cost of the $1 nuts plus the cost of the $6 nuts.
Cost of $1 nuts = 57 lbs * $1/lb = $57.
Cost of $6 nuts = x lbs * $6/lb = $6x.
The total cost of the mixture = Cost of $1 nuts + Cost of $6 nuts.
Total cost of the mixture = $57 + $6x.
Since the mixture should be worth $5 per lb, the total cost should also be equal to the total weight multiplied by $5.
Total cost of the mixture = (57 lbs + x lbs) * $5/lb.
Setting up the equation, we have:
$57 + $6x = (57 lbs + x lbs) * $5/lb.
To solve for x, let's simplify the equation:
$57 + $6x = $5(57 lbs + x lbs).
$57 + $6x = $285 + $5x.
Now, let's solve for x:
$6x - $5x = $285 - $57.
x = $228.
Randall must use 228 lbs of $6 nuts to make the mixture worth $5 per lb.