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 $8 nuts ----- x
pounds of other nuts ---- 41-x
8x + 2(41-x) = 7(41)
solve for x
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
To solve this problem, there are a few steps we need to follow:
Step 1: Assign variables:
Let's assign the variable "x" to represent the number of pounds of nuts worth $8 per lb that Randall needs to use.
Step 2: Determine the total weight of the mixture:
Randall wants to mix 41 lb of nuts with "x" lb of nuts worth $8 per lb, so the total weight of the mixture will be 41 + x lb.
Step 3: Set up the equation based on the cost per pound:
Since he wants the mixture to be worth $7 per lb, we can set up the equation:
(41 lb * $2) + (x lb * $8) = (41 + x lb) * $7
Step 4: Simplify the equation:
Simplify the equation obtained in step 3:
82 + 8x = 287 + 7x
Step 5: Solve for x:
Subtract 7x from both sides of the equation:
8x - 7x = 287 - 82
x = 205
Step 6: Answer the question:
Therefore, Randall needs to use 205 lb of nuts worth $8 per lb.
To solve this problem, we can set up a basic equation based on the given information. Let's denote the number of pounds of nuts worth $8 per pound as 'x'.
According to the problem, there are 41 pounds of nuts worth $2 per pound. So the total value of these nuts is 41 * $2 = $82.
Now, Randall wants to mix these nuts with 'x' pounds of nuts worth $8 per pound to make a mixture worth $7 per pound. The total value of 'x' pounds of nuts worth $8 per pound is 'x' * $8 = $8x.
To find the number of pounds of $8 nuts Randall needs to use, we can set up the equation:
(82 + 8x) / (41 + x) = 7
This equation represents the average value of the combination of nuts, which should be equal to the desired value of $7 per pound.
Now, let's solve the equation:
Multiplying both sides of the equation by (41 + x) to eliminate the denominator:
82 + 8x = 7 * (41 + x)
Expanding the right side:
82 + 8x = 287 + 7x
Simplifying:
8x - 7x = 287 - 82
x = 205
Therefore, Randall needs to use 205 pounds of nuts worth $8 per pound to create a mixture worth $7 per pound.