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:
[tex]1.5c+1.2p[/tex]
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:
[tex]1.5c+1.2p=1.35(c+p)[/tex]
We also know that she wants to make 20 pounds. So, c plus p must total 20. Therefore:
[tex]c+p=20[/tex]
We now have the system of equations:
[tex]\left\{ \begin{array}{ll} 1.5c+1.2p=1.35(c+p) \\ c+p=20\end{array}[/tex]
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:
[tex]c=20-p[/tex]
Let's now substitute this into the first equation:
[tex]1.5(20-p)+1.2p=1.35(20)[/tex]
Distribute:
[tex]30-1.5p+1.2p=27[/tex]
Combine like terms:
[tex]-0.3p+30=27[/tex]
Subtract 30 from both sides:
[tex]-0.3p=-3[/tex]
Divide both sides by -0.3. So, the amount of peanuts needed is:
[tex]p=10[/tex]
10 pounds of peanuts is needed.
This means that 20-10 or 10 pounds of raisins is needed.
