NC NA Create an algebraic expression from a word problem and simplify (sweets) (10+)

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Question statement

{name1} eats a lot of sweets. You are trying to work out the cost of the sweets that {name1} ate last month.

{name1} ate $\var{a1}$ lollipops, $\var{b1}$ chocolate bars and $\simplify{{c1}}$ giant jelly snakes.

You know that a chocolate bar costs $\$1$ more than a lollipop, and a giant jelly snake costs half the price of a chocolate bar.

Give any introductory information the student needs.

			Name	Type	Generated Value

a1	integer	7
b1	integer	9
c1	integer	6

			Name	Type	Generated Value

name1

string

Jerry

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xxxxxxxxxx
 
random(5..10)

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Description

Number of lollipops eaten

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Generated value: `integer`

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Let the cost of a lollipop be $\$x$.

Which is the correct algebraic expression for the overall cost of the sweets {name1} ate, in terms of $x$?

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$\simplify[]{ {a1+b1+c1/2}x + {b1+c1/2} }$

Marks: Distractor Message:
$\simplify[]{ {a1+b1+c1}x }$

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$\simplify[]{ 5x/2 + 1.5 }$

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$\simplify[]{ {a1+b1+c1/2}x + 2 }$

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Advice

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

A chocolate bar costs $\$1$ more than a lollipop, so the price of a chocolate bar can be represented by $x+1$.

A giant jelly snake costs half as much as a chocolate bar, so the price of a giant jelly snake can be represented by$\frac{1}{2}(x+1)$.

To find the total cost, multiply the expressions above for the cost of each kind of sweet by the number of sweets eaten, and add the three terms 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}

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)} &= \var{a1}x + \simplify[alwaystimes]{{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}

The correct algebraic expression for the overall cost of the sweets {name1} ate, in terms of $x$ is $\simplify[]{ {a1+b1+c1/2}x + {b1+c1/2} } \text{.}$

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NC NA Create an algebraic expression from a word problem and simplify (sweets) (10+)

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Taxonomy: mathcentre

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Taxonomy: Context

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Adelle Colbourn 4 years, 5 months ago

Adelle Colbourn 4 years, 11 months ago

Adelle Colbourn 4 years, 11 months ago

Error in variable testing condition

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Generated value: `integer`

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NC NA Create an algebraic expression from a word problem and simplify (sweets) (10+)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Adelle Colbourn 4 years, 5 months ago

Adelle Colbourn 4 years, 11 months ago

Adelle Colbourn 4 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Choose one from a list

Advanced settings

Generated value: `integer`