Question

m4l15 writing systems of equations
an order of cashews and peanuts weighs 11 pounds and costs $31.
cashews: $3.00 per pound
peanuts: $2.50 per pound
how many pounds of cashews and peanuts are in this order?
next, solve this equation for the value of p.
\

$$\begin{cases} 3c + 2.5p = 31 \\\\ c = 11 - p \\end{cases}$$

3c + 2.5p = 31
3(11 - p) + 2.5p = 31
p = \square
enter

Explanation:

Step1: Expand the left-hand side

$3(11-p)+2.5p = 33 - 3p + 2.5p = 33 - 0.5p$

Step2: Set equal to 31, isolate term with p

$33 - 0.5p = 31$
$-0.5p = 31 - 33$
$-0.5p = -2$

Step3: Solve for p

$p = \frac{-2}{-0.5}$

Answer:

$p = 4$

To find the pounds of cashews, substitute $p=4$ into $c=11-p$:
$c = 11 - 4 = 7$
So the order has 7 pounds of cashews and 4 pounds of peanuts.