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Matthew is planning a graduation party at a restaurant. Restaurant A charges $250 to reserve the room and $15 per person to eat. Restaurant B charges $370 to rent the room and $13.50 for each person to eat. How many people would Matthew need to invite for the cost at either restaurant to be the same?

Fill in the blanks to create an equation to represent the situation.

___x + 250 = 13.50x + ____

Sagot :

CintiaSalazaridn

Considering the definition of an equation and the way to solve it, Matthew would need to invite 80 people.

Definition of equation

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

  • When a value that is adding, when passing to the other member of the equation, it will subtract.
  • If a value you are subtracting goes to the other side of the equation by adding.
  • When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.
  • If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.

Number of invites

Being "x" the number of invites, and knowing that:

  • Restaurant A charges $250 to reserve the room and $15 per person to eat. → Cost restaurant A= 250 + 15x
  • Restaurant B charges $370 to rent the room and $13.50 for each person to eat. → Cost restaurant B= 370 + 13.50x

If cost at either restaurant is the same, the equation in this case is:

Cost restaurant A= Cost restaurant B

250 + 15x= 370 + 13.50x

Solving:

15x + 13.50x= 370 - 250

1.50x= 120

x= 120 ÷ 1.50

x=80

Finally, Matthew would need to invite 80 people.

Learn more about equations:

brainly.com/question/4983716

brainly.com/question/13314678

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