Create an algebraic expression from a word problem, simplify, and evaluate in dollars version

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Maria Aneiros

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Created this as a copy of Create an algebraic expression from a word problem, simplify, and evaluate.

Name	Status	Author	Last Modified
Expand brackets and collect like terms	Ready to use	Bradley Bush	20/11/2019 14:38
Create an algebraic expression from a word problem, simplify, and evaluate	Ready to use	Bradley Bush	19/12/2022 12:26
Hollie's copy of Expand brackets and collect like terms	draft	Hollie Tarr	17/09/2017 15:18
Raphael's copy of Expand brackets and collect like terms	draft	Raphael Stuhlmeier	23/11/2017 13:28
Expand brackets and collect like terms	draft	Owen Jepps	11/01/2018 06:08
samla lika termer	draft	Ida Landgärds	10/04/2018 14:19
Ida's copy of samla lika termer	draft	Ida Landgärds	10/04/2018 14:21
Ida's copy of samla lika termer	draft	Ida Landgärds	10/04/2018 14:24
Marte's copy of Expand brackets and collect like terms	draft	Marte Bråtalien	12/04/2018 11:01
Marte's copy of Expand brackets and collect like terms	draft	Marte Bråtalien	12/04/2018 11:01
Samantha's copy of Create an algebraic expression from a word problem, simplify, and evaluate	draft	Samantha Konig	28/06/2018 05:55
Samantha's copy of Create an algebraic expression from a word problem, simplify, and evaluate	draft	Samantha Konig	28/06/2018 05:56
Expand brackets and collect like terms	draft	Paul Hancock	24/07/2018 02:40
Expand brackets and collect like terms[L4 Randomised]	Needs to be tested	Matthew James Sykes	25/07/2018 13:56
Heather's copy of Expand brackets and collect like terms[L4 Randomised]	draft	Heather Driscoll	01/10/2018 15:40
Francis's copy of Expand brackets and collect like terms - two questions	draft	Francis Duah	11/11/2018 15:28
Create an algebraic expression from a word problem, simplify, and evaluate in dollars version	Ready to use	Maria Aneiros	18/05/2019 02:13
Maria's copy of Expand brackets and collect like terms	draft	Maria Aneiros	29/05/2019 05:57
Maria's copy of Create an algebraic expression from a word problem, simplify, and evaluate	draft	Maria Aneiros	29/05/2019 05:09
WordProblem01_NL	Ready to use	Paul Verheyen	28/09/2019 18:14
Musa's copy of Expand brackets	draft	Musa Mammadov	01/08/2022 08:17
Musa's copy of Expand brackets and collect like terms 3	draft	Musa Mammadov	27/06/2023 01:45
Musa's copy of 3 Expand brackets	draft	Musa Mammadov	27/06/2023 01:47

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Question statement

{name} eats a lot of sweets. You are trying to work out the cost of the sweets that {name} ate last week.

{name} ate $\var{a1}$ packets of lollipops, $\var{b1}$ packets of toffee and $\simplify{{c1}}$ packets of jelly sweets.

You know that a packet of toffee costs $1 more than a packet of lollipops, and a packet of jelly sweets costs half as much as a packet of toffees.

Give any introductory information the student needs.

			Name	Type	Generated Value

a1	integer	8
b1	integer	7
c1	integer	8

			Name	Type	Generated Value

			name	string	Jessica
			total	rational	49

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(5..10)

JME function reference

Description

Number of packets of lollipops eaten

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`

→ Used by:

b1
total

Statement
Variable testing condition
"Part b)" → "Unnamed gap" - Correct answer
"Part c)" → "Unnamed gap" - Correct answer
"Part d)" → "Unnamed gap" - Correct answer

Parts

Part a) Gap-fill
Part b) Gap-fill
1. Gap Mathematical expression
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add
Part d) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

Let the cost of a packet of lollipops be $x.

Write an expression in terms of $x$ for the cost of each kind of sweet:

Lollipops: $Gap 0.

Toffees: $Gap 1.

Jelly sweets: $Gap 2.

Advice

a)

We are told that the price of a packet of lollipops is represented by the letter $x$.

A packet of toffee costs $£1$ more than a packet of lollipops, i.e. $x+1$.

A packet of jelly sweets costs half as much as a packet of toffee, so $\frac{1}{2}(x+1)$.

b)

To find the total cost, multiply the expressions above for the cost of each kind of sweet by the number of packets eaten, and add them together.

Without simplifying, we obtain:

\begin{align}
\text{Cost} &= \simplify[]{{a1}x+{b1}(x+1) + {c1}*(1/2)*(x+1)} \\
&= \simplify[]{{a1}x+{b1}(x+1) + {c1/2}*(x+1)}
\text{.}
\end{align}

c)

The first step in simplifying this expression is to expand both sets of brackets:

\begin{align}
\simplify[]{ {a1}x + {b1}(x+1) + {c1/2}*(x+1)} &= \simplify[]{ {a1}x + {b1}x + {b1}*1 + {c1/2}x + {c1/2}*1} \\
&= \simplify[] { {a1}x + {b1}x + {b1} + {c1/2}x + {c1/2} } \text{.}
\end{align}

Finally, collect like terms:

\begin{align}
\simplify[] { {a1}x + {b1}x + {b1} + {c1/2}x + {c1/2} } &= \simplify[]{ {a1+b1+c1/2}x + {b1+c1/2} } \text{.}
\end{align}

d)

Once we know that the price of a packet of lollipops is $£2$, we can substitute this for $x$ in the equation above.

\begin{align}
\text{Cost}&=\simplify{ {a1+b1+c1/2}x+{b1+c1/2} }\\
&=\var{a1+b1+c1/2} \times 2+\var{b1+c1/2} \\
&=\var{(a1+b1+c1/2)*2+b1+c1/2} \text{.}
\end{align}

So {name} spent $£\var{total}$ on sweets last week.

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
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet

This question is used in the following exam:

Essential Maths exam by Maria Aneiros in Maria's workspace.

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Create an algebraic expression from a word problem, simplify, and evaluate in dollars version

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Maria Aneiros 5 years, 9 months ago

Maria Aneiros 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

d)

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Error

Create an algebraic expression from a word problem, simplify, and evaluate in dollars version

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Maria Aneiros 5 years, 9 months ago

Maria Aneiros 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

d)

Generated value: `integer`