Company A uses the following formula to charge a customer for a job:
$A(h) = 30 + 9.5h$,
where $A(h)$ is the cost of the job, in euro, and $h$ is the length of time that the job takes in hours - Leaving Cert Mathematics - Question 9 - 2016
Question 9
Company A uses the following formula to charge a customer for a job:
$A(h) = 30 + 9.5h$,
where $A(h)$ is the cost of the job, in euro, and $h$ is the length of ti... show full transcript
Worked Solution & Example Answer:Company A uses the following formula to charge a customer for a job:
$A(h) = 30 + 9.5h$,
where $A(h)$ is the cost of the job, in euro, and $h$ is the length of time that the job takes in hours - Leaving Cert Mathematics - Question 9 - 2016
Step 1
Complete the table below to show what Company A charges and what Company B charges for jobs that take up to 5 hours.
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Answer
Time (hours)
0
1
2
3
4
5
A(h) (€)
30
39.5
49
58.5
68
77.5
B(h) (€)
10
17.4
30.28
52.68
91.66
159.49
Step 2
On the grid below draw separate graphs to show the charge for Company A and the charge for Company B. Label each graph clearly.
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Answer
To draw the graphs:
Plot the points for Company A ((0,30),(1,39.5),(2,49),(3,58.5),(4,68),(5,77.5)).
Plot the points for Company B ((0,10),(1,17.4),(2,30.28),(3,52.68),(4,91.66),(5,159.49)).
Join the points for both graphs.
Label the Company A graph in black and the Company B graph in blue.
Step 3
Which company would charge least for a job that takes $2\frac{1}{2}$ hours to complete? Give a reason for your answer.
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Answer
Looking at the graph corresponding to 2.5 hours, Company A charges approximately 49 euros while Company B charges approximately 30.28 euros. Therefore, Company B charges least for this job.
Step 4
Use your graphs to estimate the value of $h$ for which the charge is the same for both companies.
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Answer
From the graph, the two charges intersect around h=3.2 hours.
Step 5
Find the difference in cost for a job that takes 6 hours to complete.
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Answer
Calculating for Company A:
A(6)=30+9.5(6)=30+57=87
Calculating for Company B:
B(6)=10(1.74)6≈277.52
The difference in cost is:
B(6)−A(6)=277.52−87=190.52
Thus, the difference in cost for a job that takes 6 hours to complete is approximately 190.52 euros.
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