Question

The mass of each candy in a box is 5 g. The mass of the empty box is 20 g. Let T grams

represent the total mass of the box and candies. Let n represent the number of candies, so that
� = 5� + 20.
a) Using the information above, complete the table of values below. (1 mark)
b) Graph the relation. Label and scale the axes appropriately and give the graph a title. (1
mark)
c) Based on the graph, about how many candies would be in a box that weighed 320 g? Is
this interpolation or extrapolation? (1 mark)
d) Based on the graph, about how heavy would a box with 150 candies weigh? Is this
interpolation or extrapolation? (1 mark)
n T (g)

Answer 1

Answer: a) To complete the table of values, we use the relation given:

T = 5n + 20

We can calculate T for different values of n:

n T (g)

0 20

5 45

10 70

15 95

20 120

25 145

30 170

b) Now, let's graph the relation using the values from the completed table. We'll label the axes and give the graph a title.

The x-axis represents the number of candies (n), and the y-axis represents the total mass (T in grams).

The graph will have points at (0, 20), (5, 45), (10, 70), (15, 95), (20, 120), (25, 145), and (30, 170).

c) To estimate the number of candies that would be in a box weighing 320g, we look at the graph and find the point closest to the y-value of 320. Based on the graph, it appears that there are approximately 60 candies in a box weighing 320g. This is interpolation because we are estimating within the range of values given in the table.

d) To estimate the weight of a box with 150 candies, we look at the graph and find the point closest to the x-value of 150. Based on the graph, it appears that the total mass would be approximately 770g for a box with 150 candies. This is also interpolation as we are estimating within the range of values given in the table.