Peanuts are selling for $2 per pound, and cashews are selling for $5 per pound. How much of each type of nut would be needed to create 20lb. of a mixture that would sell for $2.75 pre puund?
Use the variables, p and c, to setup a system of equations. Solve.
p=numver of pounds of peanuts
c=numver of pounds of cashews
Could someone HELP ME PLEASE I'm LOST!!!
One equation would obviousy be
p + c = 20
The other equation would be based upon the total cost. 20 lb at 2.75/per lb should cost $55.
The same amount of money must equal the costs of the two ingredients, added together.
2 p + 5 c = 55.
Solve those two equations for the answer
Since 2p + 2c = 40,
3 c = 15
c = 5
p = 15
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Of course, I'm here to help! Let's break down the problem step by step:
1. Define the variables:
Let p be the number of pounds of peanuts.
Let c be the number of pounds of cashews.
2. Write the equations based on the given information:
The first equation relates the quantities of peanuts and cashews in the mixture:
p + c = 20 (since the total weight of the mixture is 20 pounds)
The second equation deals with the prices of the nuts in the mixture:
(2 * p) + (5 * c) = 2.75 * 20 (since the cost of the mixture is $2.75 per pound and the total weight is 20 pounds)
3. Simplify the second equation:
2p + 5c = 55 (multiplying 2.75 by 20 equals 55)
4. Now we have a system of equations:
p + c = 20
2p + 5c = 55
5. Solve the system of equations using any method you prefer (substitution or elimination). For simplicity, let's use the substitution method here.
From the first equation, we can express p in terms of c:
p = 20 - c
Substitute this value for p in the second equation:
2(20 - c) + 5c = 55
40 - 2c + 5c = 55
3c = 15
c = 5
6. Substitute the value of c back into one of the original equations to find the value of p:
p + 5 = 20
p = 20 - 5
p = 15
7. Check your answer:
To validate the solution, substitute the values of p and c into the initial equations:
p + c = 20 => 15 + 5 = 20 (True)
2p + 5c = 55 => 2(15) + 5(5) = 55 (True)
Therefore, to create a 20-pound mixture that sells for $2.75 per pound, you would need 15 pounds of peanuts and 5 pounds of cashews.