Sarah mixes cashews that cost $9.00 per pound with 50 lb of peanuts that cost $5.00 per pound. How many pounds of cashews should she mix to make a nut mixture that cost $6.50 per pound?
amount of $9.00 nuts --- x lbs
9x + 5(50) = 6.5(50+x)
9x + 250 = 325 + 6x
3x = 75
x = 25
your conclusion is .... ?
To solve this problem, we can use the concept of weighted averages. The weighted average is calculated by finding the sum of the products of the values and their respective weights, and then dividing this sum by the sum of the weights.
Let's assume Sarah needs to mix x pounds of cashews with 50 pounds of peanuts.
The cashews cost $9.00 per pound, so the weight of the cashews (x) multiplied by the price per pound ($9.00) gives us the value of the cashews in the mixture: 9x.
The peanuts cost $5.00 per pound, so their weight (50) multiplied by the price per pound ($5.00) gives us the value of the peanuts in the mixture: 5 * 50 = 250.
To find the pounds of cashews needed to make a nut mixture that costs $6.50 per pound, we can set up the following equation:
(9x + 250) / (x + 50) = 6.50
We can then solve for x by multiplying both sides of the equation by (x + 50) to remove the denominator:
9x + 250 = 6.50(x + 50)
Simplifying this equation, we get:
9x + 250 = 6.50x + 325
Subtracting 6.50x from both sides and subtracting 250 from both sides, we have:
2.50x = 75
Dividing both sides by 2.50, we find:
x = 30
Therefore, Sarah needs to mix 30 pounds of cashews with 50 pounds of peanuts to make a nut mixture that costs $6.50 per pound.