Question

Ms. Corley wants to take her class on a trip to either the nature center or the zoo the nature center charges $4 per student plus $95 for a one hour naturalist program. The zoo charges $9 per student plus $75 for a 1 hour tour guide A. Solve the system of equations to represent this situation B. Solve the system of equations algebraically. Interpret the solution. C. Ms. Corley has 22 students in her class. Determine which would cost less, the nature center or the zoo

Answer 1

the answer is the nature center because it cost 183 dollars for the nature center and the zoo is 257 dollars the answer is nature center

Answer 2

A. Let the amount charged by the nature center or zoo be $y.

Let the total number of students be x.

According to the question,

The nature center charges $4 per student plus $95 for a one hour naturalist program.

`y=4x+95` (Equation 1)

The zoo charges $9 per student plus $75 for a 1 hour tour guide.

`y=9x+75` (Equation 2)

B. Solving equations 1 and 2 by substitution method.

Substituting the value of y from equation 2 in equation 1.

`9x+75=4x+95`

`5x=20`

x=4

Substituting the value of y in equation 1, we get

`y=4 *4 +95`

y = 111

Substituting the value of y in equation 2, we get

`y=9 *4 +75`

y= 111

(4,111) and (9,111) are the required solutions.

C. If there are 22 students in a class. We have to take x = 22

Charges of nature center:

`y=4x+95`

`y=4 * 22 +95`

y= $183

Charges of zoo:

`y=9x+75`

`y=9 * 22 +75`

y= $273

Since 183<273, therefore Nature center cost less.