Linear Equations
word problems
Mrs. Dyal starts the year with 150 pencils and
gives away an average of 10 pencils per week.
Represent with a function Represent with a graph
f(x)
Domain =
Range =
140
120
100
Pencils remaining
80
When will Mrs. Dual run
out of pencils?

Answer:

Part 1

The given information represented as a function, f(x) is;

f(x) = 150 - 10·x

Part 2

Please find attached the given information represented as a graph is created with Microsoft Excel

Part 3

Mrs. Dyal will run out of pencils after giving away pencils for 15 weeks

Step-by-step explanation:

The word problem relates to linear functions of the form f(x) = y = m·x + c

The given parameters are;

The number of pencils Mrs. Dyal has at the start of the year = 150 pencils

The number of pencils Mrs. Dyal gives away per week = 10 pencils

Part 1

Let "x" represent the number of weeks at which Mrs. Dyal is giving away the pencils

Given that she gives away 10 pencils each week, we have the function that represent the number of pencils remaining after "x" weeks is given as follows;

f(x) = 150 - 10×x.

The number of weeks, "x", that passes before Mrs. Dyal runs out of pencil (f(x) = 0) is given as follows;

f(x) = 0 = 150 - 10 × x

∴ 150 Pencils = 10 Pencils/Week × x

x = 150 Pencils/(10 Pencils/Week) = 15 Weeks

x = 15 Weeks

Therefore Mrs. Dyal will run out of Pencil at when x = 15 Weeks

Part 2

The function can be represented as a graph using the table of values as follows ;

Pencil remaining  [tex]{}[/tex]              Number of weeks

150                      [tex]{}[/tex]                    0

140                       [tex]{}[/tex]                    1

130                      [tex]{}[/tex]                     2

120                      [tex]{}[/tex]                     3

110                      [tex]{}[/tex]                      4

100                      [tex]{}[/tex]                     5

90                      [tex]{}[/tex]                      6

80                      [tex]{}[/tex]                      7

70                      [tex]{}[/tex]                      8

60                      [tex]{}[/tex]                      9

50                      [tex]{}[/tex]                      10

40                      [tex]{}[/tex]                      11

30                      [tex]{}[/tex]                      12

20                      [tex]{}[/tex]                      13

10                      [tex]{}[/tex]                       14

0                      [tex]{}[/tex]                        15

The domain = 0 ≤ x ≤ 15 {x ∈ N including 0}

The range = 0 ≤ f(x) ≤ 150

From the graph of the function created with Microsoft Excel, Mrs Dyal has no more Pencils left when x = 15 weeks

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