Question

Elijah bought a total of pounds of peanuts and cashew nuts and paid $49.50. If peanuts cost $2.75 per pound and cashew nuts cost $3.25 per pound, how many ponds of cashew nuts did he buy

Answer 1

Answer:

11 pounds of cashew nuts

Step-by-step explanation:

To solve this problem, we call:

p = number of pounds of peanuts bought

n = number of pounds of cashew nuts bought

We also know that:

- Each pound of peanuts costs $2.75, so the cost of p pounds of peanuts is

$2.75p$

- Each pound of cashew nuts costs $3.25, so the cost of n pounds of cashew nuts is

$3.25p$

So the total cost, which in this case is $49.50, can be written as:

$49.50=2.75p+3.25 n$ (1)

We also know that the total number of pounds is 16, so:

$16=p+n$ (2)

From this equation we get

$p=16-n$

And substituting into (1), we find n:

$49.50=2.75(16-n)+3.25n\\49.50=44-2.75n+3.25n\\5.50=0.5n\\n=\frac{5.50}{0.5}=11$

So, 11 pounds of cashew nuts.