Graphical solution of simultaneous linear equations

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Merryn Horrocks

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4 years, 7 months ago

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Name	Status	Author	Last Modified
Graphical solution of simultaneous linear equations	Ready to use	Merryn Horrocks	17/08/2020 05:36
Finding the break even point from a graph	Ready to use	Merryn Horrocks	17/08/2020 02:46

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Question statement

A {shop} owner sells {item}s for {currency(msell,"\$","")} each. It costs {currency(mcost,"\$","")} to make each {item} and {currency(bcost,"\$","")} for the equipment needed to make the {item}s.

Give any introductory information the student needs.

			Name	Type	Generated Value

shoptypes	list	List of 6 items
itemidx	integer	3
itemtypes	list	List of 6 items
msell	rational	93/10
mcost	rational	23/5
bcost	integer	500
defs	list	Nested 8×2 list
shop	string	craft shop
item	string	handmade paper
x	rational	5000/47
y	rational	46500/47

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
['bakery','bakery','bakery','craft shop','craft shop','craft shop']

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `list`

[ "bakery", "bakery", "bakery", "craft shop", "craft shop", "craft shop" ]

→ Used by:

shop

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Information only

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Write an equation to relate the income, $I$ , that is made from selling the {item}s, to the $n$ , the number of {item}s sold.

Don't enter any dollar signs, just numbers.

$I =$ Gap 0. $\times n +$ Gap 1.

Advice

The income received from selling the {item}s is the selling cost of each item multiplied by the number of items sold.

That is, $I = \var{msell} \times n$.

The equation for income is a straight line of the form $y = mx +b$, where $m$ is the gradient of the line and $b$ is the $y$-intercept.

In this equation, the constant $b = 0$ as, when 0 units are sold, $I=\$0$, so the line passes through the point $(0,0)$.

The cost to make the {item}s is the cost to make each item multiplied by the number of items made plus the fixed costs.

That is, $C = \var{mcost} \times n + \var{bcost}$.

This is also a straight line of the form $y=mx+b$

When we graph the two functions, we get the following:

{geogebra_applet("https://www.geogebra.org/m/srpxwjnu",defs)}

Your graph needs:

to start at (0,0) in the bottom left hand corner.
to show the cost line and the revenue line.
labels and arrows on both axes.
a scale on each axis.
to include the break-even point, where the two lines meet.

You may have chosen different scales for your axes. This is fine.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Information only

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Graphical solution of simultaneous linear equations

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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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

Gap-fill

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Error

Graphical solution of simultaneous linear 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

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`