Question

Gwen volunteered to work at the ticket booth for her school's Halloween carnival. The chart below gives the number of hours Gwen worked and the total number of tickets she sold.
Table
Hours (h) : 1, 2, 3, 4
Tickets (t) : 15, 30, 45, 60

Based on the table, write an equation for the relation between the number hours Gwen worked and the number of tickets she sold.

A. t = 15h
B. ht = 15
C. t = h/15
D. h = 15t​

Answer 1

A linear relation is a relationship between two variables that when the corresponding pair of values of the variables are plotted, a straight line is obtained

The equation for the relationship between hours Gwen worked and number of tickets is t = 15·h

The reason the above equation is correct is as follows:

The given parameters are;

The table of values;

Hours(h): 1, 2, 3, 4

Tickets (t): 15, 30, 45, 60

Required: To write an equation that gives the relation between the number of hours Gwen worked and the number of tickets sold

Solution:

From the given table, we have;

The common difference between successive h-values is 1

The common difference between successive t-values is 30 - 15 = 45 - 30 = 60 - 45 = 15 = Constant

Given that the common difference of the h, and t-values are constant, the relationship is a linear relationship of the form, t = m·h + c

Where;

m = The rate of change of t with h, as follows;

m = (30 - 15)/(2 - 1) = 15

∴ t - 15 = 15 × (h - 1)

t - 15 = 15·h - 15

t = 15·h - 15 + 15 = 15·h

t = 15·h

The equation for the relation between the number of hours Gwen worked and the number of tickets she sold is t = 15·h

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