Nuts worth $3 per lb are to be mixed with 8 lb of nuts worth $4.25 per lb to obtain a mixture that will be sold for $4 per lb. How many pounds of the $3 nuts should be used?
You want x where
3.00(x) + 4.25(8) = 4.00(x+8)
2 lbs of the $3 nuts should be used.
To solve this problem, we can set up a mixture equation based on the prices per pound and the desired selling price. Let's denote the number of pounds of nuts worth $3 per pound as "x".
We know that the mixture should be sold for $4 per pound, so the total value of the mixture should be equal to $4 multiplied by the total weight. The total weight of the mixture is the sum of the weights of the nuts worth $3 per pound (x lb) and the nuts worth $4.25 per pound (8 lb).
==> Total value of the mixture = $4 * (x + 8)
Additionally, the value of the nuts worth $3 per pound is equal to $3 per pound multiplied by the weight of those nuts, which is x lb.
==> Value of the $3 nuts = $3 * x
The value of the nuts worth $4.25 per pound is equal to $4.25 per pound multiplied by the weight of those nuts, which is 8 lb.
==> Value of the $4.25 nuts = $4.25 * 8
Since both the value and the weight of the mixture should be the same as the sum of the values and weights of the individual nuts, we can set up the equation:
$3 * x + $4.25 * 8 = $4 * (x + 8)
Now, we can solve this equation for x to find the number of pounds of nuts worth $3 per pound that should be used.
Let's simplify and solve the equation:
3x + 34 = 4x + 32
Subtract 3x from both sides:
34 = x + 32
Subtract 32 from both sides:
2 = x
Therefore, you should use 2 pounds of nuts worth $3 per pound to obtain the desired mixture.