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In a school event, a catering company was serving pizza to 764 people. They served 2 slices for each child and 5 slices for each adult. If the company ordered a total of 2,992 slices of pizza, how many adults and children attended the event?

Sagot :

Answer:

276 children and 488 adults attended.

Step-by-step explanation:

Setting Up a System of Equations

The problem details that the total number of people, which includes adults and children, is 764.

This means that if x represents the number of children and y for the adults the equation form is,

                                              [tex]x+y=764[/tex].

The problem also says that each child gets 2 slices, adults get 5 per and that the total number of slices is 2992. This description equates to,

                                          [tex]2x+5y=2992[/tex].

Solving the System

We can rewrite x in terms of y, solve for y and plug that value back into either equation to find the x value!

                               [tex]x+y=764\Longrightarrow x=764-y[/tex]

                                   [tex]2(764-y)+5y=2992[/tex]

                                   [tex]1528-2y+5y=2992[/tex]

                                       [tex]3y+1528=2992[/tex]

                                            [tex]3y=1464[/tex]

                                              [tex]y=488[/tex]

Solving for x, we can plug the y-value into the rearranged first equation of the system.

                                      [tex]x=764-(488)=276[/tex]

So, there were 276 children and 488 adults.

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