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The water park charges a $45 fee plus $5 per student for a field trip. The
bowling alley charges a $35 fee plus $7 per student. The lines in the graph
represent the cost of each field trip.
For what number of students will the total cost of each field trip be the same,
and what will that cost be?
Cost ($)
100
90
80
70
60
50
40
30
20
10
Field Trip Costs
y = 35+ 7x
y = 45 + 5x
1 2 3 4 5 6 7 8 9 10
Number of students

Answer :

Using linear functions, the cost will be the same, of $70, when there are 5 students.

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.

In this problem, the functions are:

  • y = 45 + 5x.
  • y = 35 + 7x.

The costs are the same when:

45 + 5x = 35 + 7x

2x = 10

x = 5.

The cost is:

y = 45 + 5 x 5 = $70.

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

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