// Numbas version: exam_results_page_options {"name": "NC NA box of chocolates ratios (10+)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "NC NA box of chocolates ratios (10+)", "tags": ["LANTITE"], "metadata": {"description": "

This question was modified from a Newcastle University question. Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students need to work out a ratio and simplify it.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "
\n
\n
\n
\n
\n
\n
\n

A family received a box of chocolates as a gift. There were five different kinds of chocolates inside: Plain, nut, caramel, dark and coconut.

", "advice": "

You are asked you to compare coconut chocolates to the rest of the box. It states that there are {c} coconut chocolates. To calculate the number of chocolates in the rest of the box, add together the stated amounts of plain, dark and nutty chocolates:

\n

$\\var{p}+\\var{d}+\\var{n}$ = $\\var{rob}$.

\n

Insert these two figures into the gaps.

\n

Coconut   $\\var{c}$ : $\\var{rob}$   Other chocolates

\n

From this, we should look to see if this answer can be simplified down. To do this, we need to find the greatest common divisor of $\\var{c}$ and $\\var{rob}$. 

\n

The greatest common divisor is $\\var{gcd2}$.

\n

Using this value to simplify the ratio by dividing each term by the value, the final answer is

\n

Coconut    $\\var{ratio_coconut}$ : $\\var{ratio_rest}$    Other chocolates.

\n

This states that for every {ratio_coconut} coconut {if(ratio_coconut=1,\"chocolate\",\"chocolates\")}, there {if(ratio_rest=1,\"is\",\"are\")} {ratio_rest} other {if(ratio_rest=1,\"chocolate\",\"chocolates\")} in the box.

\n

Therefore, it is not possible to simplify further and the final answer is 

\n

Coconut    $\\var{c}$ : $\\var{rob}$    Other chocolates.

\n

This states that for every {c} coconut {if(c=1,\"chocolate\",\"chocolates\")}, there {if(rob=1,\"is\",\"are\")} {rob} other {if(rob=1,\"chocolate\",\"chocolates\")} in the box.

\n

Note that this question contains additional information that is not required to answer the question.

", "rulesets": {}, "extensions": [], "variables": {"d": {"name": "d", "group": "Ungrouped variables", "definition": "random(1..3)*p", "description": "
\n
\n
\n
\n
\n

Number of dark chocolates on day 3.

", "templateType": "anything"}, "chocs": {"name": "chocs", "group": "Ungrouped variables", "definition": "random(70 .. 95#5)", "description": "
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n

Total number of chocolates in the box before eating.

", "templateType": "randrange"}, "ratio_rest": {"name": "ratio_rest", "group": "Ungrouped variables", "definition": "rob/gcd(c, rob)", "description": "
\n
\n
\n
\n
\n

Number of 'rest of box' chocolates in ratio of coconut to rest of box. Second part of the answer.

", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2..14 except 7 except 11 except 13)", "description": "
\n
\n
\n
\n
\n
\n
\n

Number of coconut chocolates on day 3.

", "templateType": "anything"}, "gcd2": {"name": "gcd2", "group": "Ungrouped variables", "definition": "gcd(c,rob)", "description": "
\n
\n
\n
\n
\n

The greatest common denominator of coconut and the rest of the box.

", "templateType": "anything"}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "
\n
\n
\n
\n
\n
\n
\n

Number of plain chocolates on day 3.

", "templateType": "anything"}, "rob": {"name": "rob", "group": "Ungrouped variables", "definition": "p+n+d", "description": "
\n
\n
\n
\n
\n
\n
\n
\n
\n

Sum of the rest of the box excluding coconut.

", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..14 except 7 except 11 except 13)", "description": "
\n
\n
\n
\n
\n

Number of nutty chocolates on day 3.

", "templateType": "anything"}, "ratio_coconut": {"name": "ratio_coconut", "group": "Ungrouped variables", "definition": "c/gcd(c, rob)", "description": "
\n
\n
\n
\n
\n

Number of coconut chocolates in ratio of coconut to rest of box. First part of the answer.

", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["chocs", "p", "n", "d", "c", "rob", "ratio_coconut", "ratio_rest", "gcd2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "
\n
\n
\n
\n
\n
\n
\n

The box initially contained equal numbers of each kind of chocolate, and there were $\\var{chocs}$ chocolates in the box altogether.

\n

Caramel flavoured chocolate is the family favourite, and so all of these chocolates were eaten first.

\n

Over the next few days, the remaining chocolates in the box were slowly devoured so that by the start of day three, all that remained was:

\n

$\\var{p}$ plain chocolates, $\\var{n}$ nutty chocolates, $\\var{c}$ coconut chocolates and $\\var{d}$ dark chocolates.

\n

What is the ratio of coconut chocolates to the rest of the box, at the start of day three? Give your answer in its simplest form.

\n

Coconut  [[0]] : [[1]]  Rest of the box

\n

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ratio_coconut", "maxValue": "ratio_coconut", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ratio_rest", "maxValue": "ratio_rest", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}]}], "contributors": [{"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}