Answer:
10 pounds of raisins and 10 pounds of peanuts.
Step-by-step explanation:
Let c represent the pounds of chocolate covered raisins.
Let p represent the pounds of peanuts.
We know that the raisins cost $1.50 per pound and the peanuts cost $1.20 per pound.
Ameenah wants to make 20 pounds of a mixture of the raisins and peanuts that sells for 1.35 a pound. So, we can write the following expression:
![1.5c+1.2p](https://tex.z-dn.net/?f=1.5c%2B1.2p)
This represents the cost given c pounds of raisins and p pounds of peanuts.
Ameenah wants to combine c and p to make them 1.35 per pound. In other words, the expression must equal:
![1.5c+1.2p=1.35(c+p)](https://tex.z-dn.net/?f=1.5c%2B1.2p%3D1.35%28c%2Bp%29)
We also know that she wants to make 20 pounds. So, c plus p must total 20. Therefore:
![c+p=20](https://tex.z-dn.net/?f=c%2Bp%3D20)
We now have the system of equations:
![\left\{ \begin{array}{ll} 1.5c+1.2p=1.35(c+p) \\ c+p=20\end{array}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%20%5Cbegin%7Barray%7D%7Bll%7D%201.5c%2B1.2p%3D1.35%28c%2Bp%29%20%5C%5C%20c%2Bp%3D20%5Cend%7Barray%7D)
First, since we know that c+p is 20, we can substitute that into the first equation.
Second, let's subtract p from both side for the second equation to isolate a variable. So:
![c=20-p](https://tex.z-dn.net/?f=c%3D20-p)
Let's now substitute this into the first equation:
![1.5(20-p)+1.2p=1.35(20)](https://tex.z-dn.net/?f=1.5%2820-p%29%2B1.2p%3D1.35%2820%29)
Distribute:
![30-1.5p+1.2p=27](https://tex.z-dn.net/?f=30-1.5p%2B1.2p%3D27)
Combine like terms:
![-0.3p+30=27](https://tex.z-dn.net/?f=-0.3p%2B30%3D27)
Subtract 30 from both sides:
![-0.3p=-3](https://tex.z-dn.net/?f=-0.3p%3D-3)
Divide both sides by -0.3. So, the amount of peanuts needed is:
![p=10](https://tex.z-dn.net/?f=p%3D10)
10 pounds of peanuts is needed.
This means that 20-10 or 10 pounds of raisins is needed.