theoriwade26
Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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.

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.