Question

Each school year, seventh graders who study Life Science participate in a in a special field trip to the city zoo. In 2010, the school paid $1260 for 84 students to enter the zoo. In 2011, the school paid $1050 for 70 students to enter the zoo. In 2012, the school paid $1395 for 93 students to enter the zoo.

a) Is the price the school pays each year in entree fees proportional to the number of students entering the zoo?
b) Explain why or why not.
c) Identify 1the constant of proportionality, and explain what it means in the context of this situation.
d) What would the school pay if 120 students entered the zoo?
e) How many students would enter the zoo if the school paid $1425?

Answer 1

A Yes
B $15 per student
C 15:1
D 120×15= $1800.00
E $1425÷15= 95 students

Answer 2

a. The price paid by the school each year in entrance fees is proportional to the number of students entering the zoo.

b. Because the proportion of the entrance fee paid by each student was the same, and this value was the constant k of proportionality.

c. In the expression y = k * x, "y" is the total price paid by the school, $ 15 is the entrance price for each student and "x" is the number of students participating in the field trip.

d. If 120 students entered the zoo, the school must pay $ 1800

e. If the school paid $ 1425, 95 students entered.

Explanation:

a.

If a proportional relationship is described by the set of ordered pairs that satisfies the equation y=k*x, where k is a positive constant, then k is called the constant of proportionality.

So, to determine if the price the school pays each year in entrance fees is proportional to the number of students entering the zoo, you must divide the number of students by the price paid by the school. That is, you are applying a simple rule of three: if for example in 2010 the school paid $ 1260 for 84 students, what is the price paid for 1 student? You make this same rule of three for all the years in which the excursion was made.

`(1260*1)/(84) =15`

`(1050*1)/(70) =15`

`(1395*1)/(93) =15`

As you can see, you pay $ 15 each year for each student, and as the number of students changes, the entrance fee that the school must pay varies. This means that the price paid by the school each year in entrance fees is definitely proportional to the number of students entering the zoo.

b. c.

Because the proportion of the entrance fee paid by each student was the same, and this value was the constant k of proportionality. That is, in the expression y = k * x, "y" is the total price paid by the school, $ 15 is the entrance price for each student and "x" is the number of students participating in the field trip.

d.

You should keep in mind that, as mentioned above, in the expression y = k * x, "y" is the total price paid by the school, $ 15 is the entrance price for each student and "x" is the number of students They participate in the excursion. So, if you replace "x" with the 120 students entering the zoo, you get:

y = $ 15 * 120 students

y = $ 1800

This means that if 120 students entered the zoo, the school must pay $ 1800

e.

You should keep in mind that, as mentioned above, in the expression y = k * x, "y" is the total price paid by the school, $ 15 is the entrance price for each student and "x" is the number of students They participate in the excursion. Now, if you replace "y" for $ 1425, which is the total price the school pays for "x" students, you get:

$ 1425 = $ 15 * x students

`x=(1425)/(15)`

x = 95 students

This means that if the school paid $ 1425, 95 students entered the zoo.