// Numbas version: exam_results_page_options {"name": "Rounding and estimating calculations - painting a room", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Rounding and estimating calculations - painting a room", "type": "question", "statement": "

{person['name']} just bought a new house. {capitalise(pronouns['their'])} new bedroom's wall and ceiling are currently painted white, but {pronouns['they']} would like to paint these {colour}.

\n

The dimensions of the floor are $\\var{length}\\,\\mathrm{m} \\times \\var{width}\\,\\mathrm{m}$ and the room is $\\var{height}\\,\\mathrm{m}$ high.

\n

{person['name']} want{verbs} to know how much paint to buy so {pronouns['they']} can paint all four walls and the ceiling {colour}.

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The area that can be painted with one bucket of paint.

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Overestimate and therefore we round each measurement up.

", "

Underestimate and therefore we round each measurement down.

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Is it better to overestimate or underestimate in this situation?

\n

[[0]]

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Rounding each measurement to the nearest metre, estimate the whole area to be painted {colour}.

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[[0]] m2

\n

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The room is {length}m long, {width}m wide, and {height}m high.

\n

Round each measurement in the direction you decided on above.

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Round the length to the nearest metre.

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Round the width to the nearest metre.

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Round the height to the nearest metre.

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One bucket of {colour} paint is enough to paint an area of 15m2. How many buckets should {person['name']} buy to ensure {pronouns['they']} {if(person['gender']='neutral','have','has')} enough paint?

\n

[[0]]

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Estimate the number of buckets of paint to buy, by rounding measurements of a room up to the nearest metre and estimating the total area.

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#### a)

\n

It is much better to have spare paint than not to have enough of it. So it is better to overestimate the area.

\n

Therefore, we round each measurement up.

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#### b)

\n

We round each of our measurements up to the nearest whole metre:

\n

Length: $\\var{length}\\,\\mathrm{m} \\approx \\var{l}\\,\\mathrm{m}$.

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Width: $\\var{width}\\,\\mathrm{m} \\approx \\var{w}\\,\\mathrm{m}$.

\n

Height: $\\var{height}\\,\\mathrm{m} \\approx \\var{h}\\,\\mathrm{m}$.

\n

The total area consists of five areas: two walls of $\\var{l}\\,\\text{m} \\times \\var{h}\\,\\text{m}$ (length by height); two walls of $\\var{w}\\,\\text{m} \\times \\var{h}\\,\\text{m}$ (width by height); and a ceiling of $\\var{l}\\,\\text{m} \\times \\var{w}\\,\\text{m}$ (length by width).

\n

\\\begin{align} \\var{l}\\,\\text{m} \\times \\var{h}\\,\\text{m} &= \\var{l*h}\\,\\text{m}^2 \\\\ \\var{w}\\,\\text{m} \\times \\var{h}\\,\\text{m} &= \\var{w*h}\\,\\text{m}^2 \\\\ \\var{l}\\,\\text{m} \\times \\var{w}\\,\\text{m} &= \\var{l*w}\\,\\text{m}^2 \\end{align}\

\n

Therefore, the total area {person['name']} needs to paint is

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\$\\var{2*l*h} + \\var{2*w*h} + \\var{l*w} \\,\\mathrm{m}^2 = \\var{rall}\\,\\mathrm{m}^2 \\text{.} \$

\n

#### c)

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The exact number of buckets needed is

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\$\\var{rall}\\,\\text{m}^2 \\div 15\\,\\text{m}^2 = \\var{rall/15} \\text{.}\$

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{person['name']} can only buy a whole number of buckets, so {pronouns['they']} need{verbs} to decide between {buckets-1} and {buckets} paint buckets. As it is better to buy more paint than not buy enough, {pronouns['they']} should buy {buckets} buckets of {colour} paint.

", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}