Elijah bought a total of 16 pounds of peanuts and cashew nuts and paid 49.50. If peanuts cost 2.75 dollars per pound, and cashew nuts cost 3.25 dollars per pound how many pounds of cashew nuts did he buy

The answer to your question is  He bought 11 pounds of cashew.

Step-by-step explanation:

Data

Total pounds = 16

peanuts = p = $2.75

cashew = c = $3.25

total cost = $49.5

Process

1.- Write two equations to solve this problem

                   p  +  c = 16                    Equation 1

            2.75p + 3.25c = 49.50        Equation 2

Solve the system by substitution

2.- Solve equation 1 for p

                   p = 16 - c

Substitute p in equation 2

            2.75(16 - c) + 3.25c = 49.5

Expand

             44 - 2.75c + 3.25c = 49.5

Solve for c

              3.25c - 2.75c = 49.5 - 44

                          0.5c = 5.5

                                c = 5.5/0.5

                                c = 11

3.- Find p

                  p = 16 - 11

                  p = 5 pounds

4.- Conclusion

Ellijah bought 11 pounds of cashew and 5 pounds of peanuts                        

she bought 11 pounds of cashew nuts.

Step-by-step explanation:

Let x represent the number of peanuts that she bought.

Let y represent the number if cashew nuts that she bought.

Elijah bought a total of 16 pounds of peanuts and cashew nuts. This means that

x + y = 16

If peanuts cost 2.75 dollars per pound, and cashew nuts cost 3.25 dollars per pound and she paid 49.50 for all she bought, it means that

2.75x + 3.25y = 49.5 - - - - - - - - - 1

Substituting x = 16 - y into equation 1, it becomes

2.75(16 - y) + 3.25y = 49.5

44 - 2.75y + 3.25y = 49.5

- 2.75y + 3.25y = 49.5 - 44

0.5y = 5.5

y = 5.5/0.5

y = 11

x = 16 - y = 16 - 11

x = 5