Question

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

Answer 1

To solve this problem, we can set up a system of equations. Let C represent the number of children and A represent the number of adults. From the given information, we know that the total number of people attending the event is 764, and that the company ordered a total of 2992 forks. We can use these equations to solve for the number of children and adults.

Step-by-step explanation:

To solve this problem, we can set up a system of equations.

Let C represent the number of children and A represent the number of adults.

From the given information, we know that the total number of people attending the event is 764, so we can write the equation:

C + A = 764

We also know that 2 forks are needed for each child and 5 forks are needed for each adult. The total number of forks ordered is 2992, so we can write the equation:

2C + 5A = 2992

We now have a system of equations that can be solved to find the values of C and A.

By solving these equations, we can determine the number of children and adults attending the event.

Answer 2

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