Elijah brought a total of 16 pounds of peanuts and cashew nuts and paid $49.50 if peanuts cost $2.75 per pound and cashews nuts cost $3.25 per pound how many pounds of cashews nuts did he buy

The number of pounds of cashew is 11

Step-by-step explanation:

Let P represent the peanut

Let C represent the cashew nut.

From question, we were told that Elijah brought a total of 16 pounds of peanuts and cashew nuts. This can be written as:

P + C = 16 (1)

The total cost = $49.50

Cost per peanut = $2.75

Cost per cashew = $3.25

The above can be represented as:

49.50 = 2.75P + 3.25C. (2)

From equation 1,

P + C = 16

P = 16 - C

Substitute the value of P into equation 2:

49.50 = 2.75P + 3.25C.

49.50 = 2.75 (16 - C) + 3.25C

49.50 = 44 - 2.75C + 3.25C

49.50 = 44 + 0.5C

Collect like terms

49.50 - 44 = 0.5C

5.5 = 0.5C

Divide both side by 0.5

C = 5.5/0.5

C = 11

Therefore, the number of pounds of cashew is 11