// Numbas version: exam_results_page_options {"name": "NC NA Write an algebraic expression from a word problem (overtime) (10+)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "NC NA Write an algebraic expression from a word problem (overtime) (10+)", "tags": ["LANTITE"], "metadata": {"description": "

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given the total hours of work (randomised) and overtime (randomised) and asked to write an expression for the amount of pay earned.

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$H$ is used to represent a standard hourly rate of pay in dollars.

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First work out how many hours were worked at the standard hourly rate. {total_hours} - {over_time} = {normal_hours}

{normal_hours} is multiplied by H to give the amount earned during standard hours. {normal_hours} x H = {normal_hours}H

{normal_hours}H is earned during the standard hours.

H is multiplied by 1.5 for each overtime hour, which is paid at time and a half. There are {over_time} overtime hours, so {over_time} x 1.5 x H = {1.5*over_time}H

{1.5*over_time}H is earned during the overtime hours.

Then the standard pay and the overtime pay are added: {normal_hours}H + {1.5*over_time}H = {normal_hours+1.5*over_time}H

{normal_hours+1.5*over_time}H represents the amount earned after {total_hours} hours work.

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Number of hours paid at the standard rate. Student are required to work this out. It is set up to be greater than or equal to over_time.

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Overtime hours worked. This is stated in the question. It is set up to be less than or equal to normal_hours.

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Total hours worked. This is stated in the question, but calculated from the other two variables.

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Which one of the following expressions would represent the amount of pay earned for {total_hours} hours work, where {over_time} of those hours were worked at time-and-a-half (that is at 1.5 times the standard rate of pay)?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\var{total_hours+over_time}H$", "$\\var{normal_hours+1.5*over_time}H$", "$ \\frac{\\var{total_hours}}{1.5}H$", "$\\var{total_hours+1.5*over_time}H$"], "matrix": [0, "1", 0, 0], "distractors": ["How many hours were worked at the normal rate? Click on Reveal Answer and scroll down for Advice regarding this question.", "Well done!", "Does dividing by 1.5 increase the amount paid? Click on Reveal Answer and scroll down for Advice regarding this question.", "How many hours were worked at the normal rate? Click on Reveal Answer and scroll down for Advice regarding this question."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}