Ruairi has a weekend job - Junior Cycle Mathematics - Question 11 - 2019
Question 11
Ruairi has a weekend job. His total pay per day is a fixed rate plus tips. The tips are a percentage of the customer spend.
The graph below shows Ruairi’s total pay ... show full transcript
Worked Solution & Example Answer:Ruairi has a weekend job - Junior Cycle Mathematics - Question 11 - 2019
Step 1
What is Ruairi’s fixed rate per day (his pay when the customer spend is €0)?
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Answer
Ruairi's fixed rate per day, when the customer spend is €0, is €80. This is indicated by the y-intercept on the graph, where R intersects the y-axis.
Step 2
What was Ruairi’s total pay on that day?
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Answer
On that day, when the customer spend was €500 (S = 5), Ruairi’s total pay was €130. This can be calculated using the equation derived from the graph.
Step 3
How much was Ruairi paid in tips on that day?
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Answer
Ruairi was paid €50 in tips on that day. This is calculated by taking the total pay of €130 and subtracting the fixed rate of €80.
Step 4
Explain what this means in the context of Ruairi’s total pay and the customer spend.
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Answer
The point (2, 105) on the graph indicates that when the customer spend is €200 (since S is in hundreds), Ruairi’s total pay is €105. This shows the relationship between the customer spend and his total earnings, revealing that a portion of his total pay comes from tips.
Step 5
Tick (✓) the correct box to show which one corresponds to the graph of Ruairi’s total pay. Tick one box only. Justify your answer.
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Answer
The correct equation corresponding to the graph of Ruairi's total pay is R = 80 + 10S. This is because the y-intercept is €80 (the fixed rate) and the slope indicates that for every additional €100 in customer spend, Ruairi earns an additional €10.
Step 6
Draw the graph of Cillian’s pay, C, on the axes below, for 0 ≤ S ≤ 5 and S ∈ R.
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To draw Cillian's graph, first note the equation C = 60 + 20S. This gives a y-intercept of €60 and a slope of 20. Plot points for S = 0 (60), S = 1 (80), S = 2 (100), S = 3 (120), S = 4 (140), and S = 5 (160) to draw a line connecting these points.
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