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Kiara and Donovon attend different middle schools. They both went to their schools’ winter carnivals. Kiara paid a $5 entrance fee and bought several tickets costing $0.75 each for games and rides. Donovon paid a $7 entrance fee and bought several tickets costing $0.50 each for games and rides. How many tickets, , must Kiara and Donovan each buy in order for the cost of attending their school carnivals to be the same?

Sagot :

Using linear functions, it is found that they have to buy 8 tickets for the costs to be the same.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For the functions in this problem, we consider that:

  • The entrance fee is the intercept.
  • The cost for carnivals(games/rides) is the slope.

Hence the cost functions for Kiara and Donovon are given, respectively, by:

  • K(x) = 5 + 0.75x.
  • D(x) = 7 + 0.5x.

The costs will be the same when:

K(x) = D(x)

5 + 0.75x = 7 + 0.5x.

0.25x = 2

x = 2/0.25

x = 8.

They have to buy 8 tickets for the costs to be the same.

More can be learned about linear functions at https://brainly.com/question/24808124

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