Question

HELP

You are paying for a group of people to attend the state fair. Your total cost is proportional to the number of people in the group. Let C denote your total cost in dollars and n the number of people in the group.

a) (1 point) Write an equation that shows the proportionality relation. Let 14 be the constant of proportionality.

b) (1 point) What, in practical terms, does the constant of proportionality represent in this case? Circle your answer.
a) It is the number of people attending the fair.
b) It is the total cost of the fair.
c) It is the cost of attending per person.
d) It cannot be determined.​

Answer 1

(a) C = 14n

(b) c -- the cost of attending per person

Explanation:

The equation for a proportion is written ...

y = kx

Here, we have C given as the dependent variable, and n as the independent variable. The constant of proportionality, k, is said to be 14. Then the desired equation is ...

C = 14k

__

Units analysis tells you the meaning of k. The units in this equation are given as ...

cost in dollars = 14 × number of people

Dividing by the coefficient of 14, we see what its units are:

(cost in dollars)/(number of people) = 14 = cost/person

The constant 14 represents the cost of attending per person.