Solution of a word problem using graphical simultaneous equations.

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Name	Status	Author	Last Modified
Solution of a word problem using graphical simultaneous equations.	Ready to use	Merryn Horrocks	18/08/2020 12:45
word problem using graphical simultaneous equations 2.	Ready to use	Merryn Horrocks	19/08/2020 09:30

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Question statement

A gym offers casual visits and memberships.

For a casual visit, you pay a fixed amount each time you visit the gym.

For a membership, you pay an upfront fee, and then a smaller amount each time you visit the gym.

The graph the relationship between cost (in dollars) ( $y$ ) and number of visits to the gym ( $x$ ) for the two programs.

{geogebra_applet('https://www.geogebra.org/m/uky4vz3z',defs)}

Give any introductory information the student needs.

			Name	Type	Generated Value

defs	list	Nested 8×2 list
m1	integer	25
m2	rational	20
b2	integer	50
xmax	number	15
k	integer	10
ymax	number	375
visits1	integer	12
gymwins	integer	-1
visittype	integer	1

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
[
  ['b1',0],['m1',m1],['b2',b2],['m2',m2],
  ['xmin',0],['xmax',xmax],['ymin',0],['ymax',ymax]
  ]

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `list`

[ [ "b1", 0 ], [ "m1", 25 ], [ "b2", 50 ], [ "m2", 20 ], [ "xmin", 0 ], [ "xmax", 15 ], [ "ymin", 0 ], [ "ymax", 375 ] ]

← Depends on:

b2
m1
m2
xmax
ymax

→ Used by:

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Which line represents the gym membership option?

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red line

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The red line represents the gym membership option because the line has a non-zero $y$-intercept which represents the value of the upfront payment.

If you intend to visit the gym {visits1} times, the cheaper option is using casual visits because this line has a lower value at the point where $x=\var{visits1}$ the cheaper option is using a gym membership because this line has a lower value at the point where $x=\var{visits1}$ it doesn't matter which option you choose because the cost is the same.

The fewest number of visits for which it is cheaper to take out a gym membership is {k+gymwins}. This is the first $x$-axis value for which the gym membership line is below the casual visit line.

The most number of visits for which it is cheaper to pay for casual visits is {k+gymwins}. This the last $x$-axis value for which the casual visit line is below the gym membership line.

{k} visits are required for the cost of a gym membership to equal the cost of the casual visits. This is the point at which the two lines intersect.

The cost of the upfront payment for gym membership is the point at which the gym membership line cuts the $y$-axis, which is at \${b2}.

The cost of entry to the gym on a casual visit is the gradient of the casual visit line. It is also the value of the casual visit line when $x$=1 (1 visit). This is equal to {m1}.

The cost of entry to the gym if you own a membership is the gradient of the gym membership line. This is given by vertical rise over horizontal run and is equal to {m2}.

The graph is only meaningful at points where $x$ is a whole number because you cannot have fractional visits to the gym. For example, you cannot visit the gym 6.7 times.

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Solution of a word problem using graphical simultaneous equations.

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Taxonomy: mathcentre

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Taxonomy: Context

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Merryn Horrocks 4 years, 7 months ago

Merryn Horrocks 4 years, 7 months ago

Merryn Horrocks 4 years, 7 months ago

Error in variable testing condition

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Generated value: `list`

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Solution of a word problem using graphical simultaneous equations.

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Merryn Horrocks 4 years, 7 months ago

Merryn Horrocks 4 years, 7 months ago

Merryn Horrocks 4 years, 7 months ago

Error in variable testing condition

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Generated value: list

Parts

Choose one from a list

Advanced settings

Generated value: `list`