// Numbas version: exam_results_page_options {"name": "Samantha's copy of Create an algebraic expression from a word problem, simplify, and evaluate", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "

Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

", "licence": "Creative Commons Attribution 4.0 International"}, "tags": ["algebraic expressions", "collect terms", "create algebraic expressions", "simplify algebraic expressions", "simplifying algebraic expressions", "taxonomy"], "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.

", "functions": {}, "variables": {"b1": {"definition": "random(2..10 except a1)", "group": "Number of packets eaten", "templateType": "anything", "description": "

Number of packets of toffee eaten

", "name": "b1"}, "name": {"definition": "random('Jerry','Jessica')", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "name"}, "c1": {"definition": "random(2..5)*2", "group": "Number of packets eaten", "templateType": "anything", "description": "

Number of packets of jelly sweets eaten.

", "name": "c1"}, "total": {"definition": "(a1+b1+c1/2)*2 + b1+c1/2", "group": "Ungrouped variables", "templateType": "anything", "description": "

The total spent.

", "name": "total"}, "a1": {"definition": "random(5..10)", "group": "Number of packets eaten", "templateType": "anything", "description": "

Number of packets of lollipops eaten

", "name": "a1"}}, "name": "Samantha's copy of Create an algebraic expression from a word problem, simplify, and evaluate", "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.

", "variable_groups": [{"name": "Number of packets eaten", "variables": ["a1", "b1", "c1"]}], "extensions": ["stats"], "parts": [{"showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "

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: £[[0]]

Toffees: £[[1]]

Jelly sweets: £[[2]]

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Write an algebraic expression for the overall cost of the sweets {name} ate, in terms of $x$.

£[[0]]

Now simplify your expression for the total cost.

£[[0]]

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You find out that a packet of lollipops costs $£2$.

Calculate {name}'s total expenditure on sweets last week.

£[[0]]

Don't use brackets

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