Question

A catering company is setting up tables 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,a and the number of children,c and solve to find out how many of each attended the event

Answer 1

488 adults and 276 children

Explanation:

So, we need two linear equations here to start, and we do have them.

Our first linear equation tells us how we get the number of forks:

2c + 5a = 2992

And the second tells us the number of people there:

c + a = 764

I will solve this using substitution. We start by minusing a from both sides in the second equation, giving us:

c = 764 - a

Then, we will substitute this into our first equation, giving us:

2(764 - a) + 5a = 2992

Then, we will open the parentheses, giving us:

1528 - 2a + 5a = 2992

Combining like terms and subtracting 1528 from both sides gives us:

3a = 1464

Dividing by 3:

a = 488

So there were 488 adults. Then, we take our original second equation and substitute 488 for a, giving us:

488 + c = 764

Minus 488 from both sides gives us:

c = 276

So, there were 276 children. In total, we had 488 adults and 276 children.

Hope this helped!