Question

At the candy shop, Ameenah sells chocolate covered raisins, c, for $1.50 per pound, and peanuts, p, for $1.20 per pound. Ameenah wants to make 20 pounds of a mixture of raisins and peanuts that sells for $1.35 a pound. How many pounds of each should she use?
Thanks! :)

Answer 1

Answer:

10 pounds of both raisins and peanuts.

Step-by-step explanation:

Answer 2

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:

$1.5c+1.2p$

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:

$1.5c+1.2p=1.35(c+p)$

We also know that she wants to make 20 pounds. So, c plus p must total 20. Therefore:

$c+p=20$

We now have the system of equations:

$\left\{ \begin{array}{ll} 1.5c+1.2p=1.35(c+p) \\ c+p=20\end{array}$

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:

$c=20-p$

Let's now substitute this into the first equation:

$1.5(20-p)+1.2p=1.35(20)$

Distribute:

$30-1.5p+1.2p=27$

Combine like terms:

$-0.3p+30=27$

Subtract 30 from both sides:

$-0.3p=-3$

Divide both sides by -0.3. So, the amount of peanuts needed is:

$p=10$

10 pounds of peanuts is needed.

This means that 20-10 or 10 pounds of raisins is needed.