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6 months, 4 weeks ago

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Question statement

{capitalise(written_number(n))} {pluralise(n, "year", "years")} ago, {nameB} was {written_number(p)} times older than {nameA}.

In {written_number(m)} years' time, {nameC} will be {written_number(q)} times older than {nameB}.

Today, the sum of the ages of {nameA}, {nameB} and {nameC} is {total}.

Calculate the age of each person.

Give any introductory information the student needs.

			Name	Type	Generated Value

nameA	string	Riley
ageA	integer	7
xA	expression	R

			Name	Type	Generated Value

nameB	string	Henry
ageB	integer	12
xB	expression	H

			Name	Type	Generated Value

nameC	string	Quinn
ageC	integer	26
xC	expression	Q

			Name	Type	Generated Value

names	list	List of 3 items
n	integer	2
m	integer	2
p	integer	2
q	integer	2
total	integer	45

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
names[0]['name']

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: `string`

Riley

← Depends on:

names

→ Used by:

Statement
Advice
"Unnamed part" - prompt

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add

Gap-fill

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

{nameA}: Gap 0.

{nameB}: Gap 1.

{nameC}: Gap 2.

Advice

Let $\var{xA}$ be {nameA}'s age, $\var{xB}$ be {nameB}'s age and $\var{xC}$ be {nameC}'s age.

{capitalise(written_number(n))} {pluralise(n, "year", "years")} ago, everyone was {n} {pluralise(n, "year", "years")} younger, so {nameB} was $\var{xB}-\var{n}$ and {nameA} was $\var{xA}-\var{n}$ . At that time, {nameB} was {p} times older than {nameA}, i.e.

$\var{xB}-\var{n}=\simplify{{p}*({xA}-{n})}$

Expand and simplify:

$\var{xB}=\simplify{{p}*{xA}-{(p-1)*n}}\tag{1}$

In {written_number(m)} years' time, everyone will be {m} {pluralise(m, "year", "years")} older, so {nameC} will be $\var{xC}+\var{m}$ and {nameB} will be $\var{xB}+\var{m}$ . At that time, {nameC} will be {q} times older than {nameB}, i.e.

$\var{xC}+\var{m}=\simplify{{q}*({xB}+{m})}$

Expanding and simplifying gives $\var{xC}=\simplify{{q}*{xB}+{(q-1)*m}}$ . Now use (1) to write $\var{xC}$ in terms of $\var{xA}$ :

$\var{xC}=\simplify{{q}*({p}*{xA}-{(p-1)*n})+{(q-1)*m}}=\simplify{{q*p}*{xA}-{q*(p-1)*n-(q-1)*m}}\tag{2}$

The sum of their ages is {total}, i.e.

$\var{xA}+\var{xB}+\var{xC}=\var{total}$

From (1) and (2) above,

$\var{xA}+\simplify{{p}*{xA}-{(p-1)*n}}+\simplify{{q*p}*{xA}-{q*(p-1)*n-(q-1)*m}}=\var{total}$

which simplifies to

$\simplify{{p+1+p*q}*{xA}-{n*(p-1)*(q+1)-m*(q-1)}}=\var{total}$

Solving this gives $\var{xA}=\var{ageA}$ . Substituting this into (1) gives $\var{xB}=\var{ageB}$ , and substituting it into (2) gives $\var{xC}=\var{ageC}$ .

Therefore {nameA} is {ageA}, {nameB} is {ageB} and {nameC} is {ageC}.

Give a worked solution to the whole question.

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Part	Test	Passed?
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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Martin Jones 6 months, 4 weeks ago

Martin Jones 6 months, 4 weeks ago

Martin Jones 6 months, 4 weeks ago

Error in variable testing condition

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Generated value: `string`

Parts

Gap-fill

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Error

Ages problem

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Martin Jones 6 months, 4 weeks ago

Martin Jones 6 months, 4 weeks ago

Martin Jones 6 months, 4 weeks ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`