Randall wants to mix 41 lb of nuts worth $2 per lb with some nuts worth $8 per lb to make a mixture worth $7 per lb. How many pounds of $8 nuts must he use?
Pounds of nuts-cost per pound-total cost
41-$2-?
x-$8-?
?-$7-?
There is a chart and I have to fill in the question marks. x= 205/6 0r 34.16667
2*41 + 8x = 7(41+x)
it's going to take a lot of $8 nuts to bring the price up to $7/lb from $2/lb.
To determine the number of pounds of $8 nuts Randall must use, we can set up an equation using the information provided.
Let's assume he uses x pounds of $8 nuts.
The total weight of nuts can be expressed as:
41 lb + x lb = total weight
The cost of the $2 nuts can be expressed as:
41 lb * $2/lb = $82
The cost of the $8 nuts can be expressed as:
x lb * $8/lb = $8x
The total cost of the mixture can be expressed as:
(total weight) * ($7/lb) = ($7 * (41 + x))
Using the equation: $82 + $8x = $7 * (41 + x)
Simplifying the equation: $82 + $8x = $287 + $7x
Subtracting $7x from both sides: $8x - $7x = $287 - $82
Simplifying further: $x = $205/6
Therefore, Randall must use approximately 34.16667 pounds of $8 nuts.
To find the number of pounds of $8 nuts that Randall needs to use, we can set up an equation based on the total cost of the mixture.
Let's consider the total cost of the nuts worth $2 per pound first. Since Randall wants to mix 41 pounds of these nuts, the total cost is given by:
(41 pounds) x ($2 per pound) = $82
Now, let's represent the number of pounds of $8 nuts as "x". The total cost of these nuts is given by:
(x pounds) x ($8 per pound) = $8x
Since Randall wants the mixture to have a total cost of $7 per pound, we can set up the equation:
Total cost of $2 nuts + Total cost of $8 nuts = Total cost of the mixture
$82 + $8x = (41 + x) pounds x ($7 per pound)
Simplifying this equation, we have:
82 + 8x = 287 + 7x
Combine like terms:
8x - 7x = 287 - 82
x = 205
Therefore, Randall must use 205/6 pounds (approximately 34.16667 pounds) of $8 nuts in order to achieve the desired mixture.