The catering company is setting the table for a big event that will host 764 people when they set up the tables they need 2 forks for each child and 5 forks for each adult the company ordered a total of 2992 forks set up a system of equations involving the number of adults and the number of children C to solve to find out how many of each attended the event

Given:

child = 2 forks

adult = 5 forks

total number of forks = 2992

total number of people = 764

c + a = 764

2c + 5a = 2992

find the value of c using the 1st equation.

c = 764 - a

substitute c in the 2nd equation by its value

2c + 5a = 2992

2 (764-a) + 5a = 2992

1528 - 2a + 5a = 2992

1528 + 3a = 2992

3a = 2992 - 1528

3a = 1464

3a/3 = 1464/3

a = 488

c = 764 - a

c = 764 - 488

c = 276

child = 276; adult = 488

2c + 5a = 2992

2 (276) + 5 (488) = 2992

552 + 2440 = 2992

2992 = 2992