Cashews sell for $4.00 per pound and peanuts for $1.50 per pound. The peanuts didn't sell well, so in order to sell 60 lbs of peanuts the manager decided to mix 60 lbs of peanuts w/ cashews and sell the mixture for $2.50 per pound. How many lbs cashews should be mixedto ensure no change in profit?
I thought the equation would be
4c + 1.50p = 2.50
c + 60p = 100 ?
or should I multiply 2.50(60)
total cost=sum of costs
2.50(c+p)=4c + 1.50p
and p is given as 60
solve for c
A store is selling two mixtures of nuts in 20-ounce bags. The first mixture has 15 ounces of peanuts combined with five ounces of cashews, and costs $4.25. The second mixture has five ounces of peanuts and 15 ounces of cashews, and costs $6.75. How much does one ounce of peanuts and one ounce of cashews cost?
To solve this problem, you should multiply $2.50 by 60 because the goal is to find the mixture price for selling the 60 pounds of peanuts and cashews.
So, 2.50 * 60 = $150.
Now let's set up the equations to find the quantity of cashews to be mixed:
Let c represent the weight (in pounds) of cashews and p represent the weight (in pounds) of peanuts.
The cost equation (based on the price per pound) would be: 4c + 1.50p = 150.
Since the goal is to ensure no change in profit, the equation for the weight of cashews mixed should be: c + p = 60.
Now we can solve these equations simultaneously to find the value of c.
To determine how many pounds of cashews should be mixed to ensure no change in profit, we can set up a system of equations based on the given information.
Let's assign variables to the quantities mentioned:
c = pounds of cashews
p = pounds of peanuts
According to the given information, cashews sell for $4.00 per pound, peanuts sell for $1.50 per pound, and the mixture sells for $2.50 per pound.
To determine the equation for the total selling price, we can use the following formula:
Total Selling Price = Price of Cashews + Price of Peanuts
For the cashews:
Price of Cashews = $4.00 per pound * c pounds = 4c
For the peanuts:
Price of Peanuts = $1.50 per pound * p pounds = 1.5p
Since a total of 60 pounds of peanuts are being mixed with cashews, we can also create another equation regarding the weight of the mixture:
p + c = 60
Lastly, the manager aims to sell the mixture for $2.50 per pound. Therefore, we can create another equation based on the selling price:
Total Selling Price = $2.50 * 60 = 150
Now we have three equations:
1. 4c + 1.5p = Total Selling Price
2. p + c = 60
3. Total Selling Price = 150
To solve this system of equations, we can substitute equation 3 into equation 1:
4c + 1.5p = 150
Next, rearrange equation 2 to solve for p:
p = 60 - c
Substitute this value of p into the equation:
4c + 1.5(60 - c) = 150
Now we can solve for c:
4c + 90 - 1.5c = 150
2.5c = 60
c = 24
Therefore, 24 pounds of cashews should be mixed with 36 pounds of peanuts to ensure no change in profit.