Percentages and ratios - box of chocolates - Numbas at mathcentre.ac.uk

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Adelle Colbourn 5 years, 7 months ago

Created this as a copy of Percentages and ratios - box of chocolates.

Name	Status	Author	Last Modified
Percentages and ratios - box of chocolates	Ready to use	Lauren Richards	20/11/2019 14:41
Marte's copy of Percentages and ratios - box of chocolates	draft	Marte Bråtalien	12/04/2018 11:01
Maria's copy of Percentages and ratios - box of chocolates	draft	Maria Aneiros	29/05/2019 05:48
Percentages and ratios - box of chocolates	draft	Adelle Colbourn	13/08/2020 00:49
Ugur's copy of Percentages and ratios - box of chocolates	Ready to use	Ugur Efem	12/01/2022 11:45

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Question statement

A family receive a box of chocolates as a gift. There are five different kinds of chocolate inside: plain, nut, caramel, dark and coconut.

The box contains equal numbers of each kind of chocolate..

Give any introductory information the student needs.

			Name	Type	Generated Value

chocs	integer	95
type	rational	19
p	integer	2
n	integer	3
d	integer	2
c	integer	1
rob	integer	7
prob	decimal	dec("0.38")
a	integer	8
perc	number	38
minusc	rational	76
ratio_plain	number	1
ratio_dark	number	1
ratio_coconut	number	1
ratio_rest	number	7
gcd	number	2
gcd2	number	1

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

Total number of chocolates in the box before eating.

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

Can an exam override the value of this variable?

Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add
Part c) Gap-fill
1. Gap Number entry
  Add
Part d) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add

Gap-fill

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

What percentage of the box of chocolates is represented by the caramel chocolates?

Caramel chocolate = Unnamed gap % of the box.

Advice

a)

100% represents the whole box of chocolates. As there are 5 different kinds of chocolate in the box and they are all represented equally, to calculate the percentage chocolates which are caramel, divide 100 by 5.

Caramel chocolate = $\displaystyle\frac{100}{5}$ = $20$ % of the box.

The original number of chocolates in the box is stated. We worked out above that each type of chocolate makes up 20% of the box, so we need to work out 20% of {chocs}.

To do this, either divide {chocs} by 100 and multiply by 20, OR multiply {chocs} by 0.2. The two methods will give the same result.

Method 1: $\displaystyle\frac{\var{chocs}}{100}$ x $20$ = $\var{type}$ ;

Method 2: $\var{chocs}$ x $0.2$ = $\var{type}$ .

There are now {type} fewer chocolates in the box, but the remaining chocolates now represent 100% of the box. There are now only 4 types of chocolate in it and there is still equal representation inside the box.

Use the method from part a) to find out the equal share of each chocolate type.

Each type = $\displaystyle\frac{100}{4}$ = $25$ % of the box.

The first section asks you to compare plain chocolate and dark chocolate. It states that there are {p} plain chocolates and {d} dark chocolates left in the box.

Insert the numbers of each into the gaps.

Plain $\var{p}$ : $\var{d}$ Dark

From this, we should look to see if this answer can be simplified down. To do this, we need to find the greatest common divisor of $\var{p}$ and $\var{d}$ .

The greatest common divisor is $\var{gcd}$ .

Using this value to simplify down the ratio by dividing each term by the value, the final answer is

Plain $\var{ratio_plain}$ : $\var{ratio_dark}$ Dark.

This states that for every {ratio_plain} plain {if(ratio_plain=1,"chocolate","chocolates")}, there {if(ratio_dark=1,"is","are")} {ratio_dark} dark {if(ratio_dark=1,"chocolate","chocolates")}.

Therefore, it is not possible to simplify further and the final answer is

Plain $\var{p}$ : $\var{d}$ Dark.

This states that for every {p} plain {if(p=1,"chocolate","chocolates")}, there {if(d=1,"is","are")}{d} dark {if(d=1,"chocolate","chocolates")}.

ii)

The second section asks you to compare coconut chocolates and the rest of the box. It states that there are {c} coconut chocolates. To calculate the number of chocolates in the rest of the box, add together the stated amounts of plain, dark and nutty chocolates:

$\var{p}+\var{d}+\var{n}$ = $\var{rob}$ .

Insert these two figures into the gaps.

Coconut $\var{c}$ : $\var{rob}$ Other chocolates

From this, we should look to see if this answer can be simplified down. To do this, we need to find the greatest common divisor of $\var{c}$ and $\var{rob}$ .

The greatest common divisor is $\var{gcd2}$ .

Using this value to simplify down the ratio by dividing each term by the value, the final answer is

Coconut $\var{ratio_coconut}$ : $\var{ratio_rest}$ Other chocolates.

This states that for every {ratio_coconut} coconut {if(ratio_coconut=1,"chocolate","chocolates")}, there {if(ratio_rest=1,"is","are")} {ratio_rest} other {if(ratio_rest=1,"chocolate","chocolates")} in the box.

Therefore, it is not possible to simplify further and the final answer is

Coconut $\var{c}$ : $\var{rob}$ Other chocolates.

This states that for every {c} coconut {if(c=1,"chocolate","chocolates")}, there {if(rob=1,"is","are")} {rob} other {if(rob=1,"chocolate","chocolates")} in the box.

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:

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Percentages and ratios - box of chocolates

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Taxonomy: mathcentre

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Taxonomy: Context

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Adelle Colbourn 5 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

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Percentages and ratios - box of chocolates

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Adelle Colbourn 5 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

Generated value: `integer`