Leaving Cert Mathematics Algebra: Emma works part time after schoo

Emma works part time after school at the local takeaway - Leaving Cert Mathematics - Question 1 - 2016

Question 1

Emma works part time after school at the local takeaway. She is paid a rate per hour and also receives €2 for each delivery she makes. (a) One day, she works for 2 ... show full transcript

Worked Solution & Example Answer:Emma works part time after school at the local takeaway - Leaving Cert Mathematics - Question 1 - 2016

Step 1

One day, she works for 2 hours, makes 5 deliveries and is paid a total of €28. Find her hourly rate of pay.

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Answer

To find Emma's hourly rate of pay, we start by defining variables:

Let the hourly rate be denoted as $x$ .
For 2 hours of work, her earnings from the hourly rate can be calculated as:

$2x$

Additionally, for 5 deliveries, she earns:

$5 imes 2 = 10$

Thus, her total earnings can be expressed as:

$2x + 10 = 28$

Rearranging the equation gives:

$2x = 28 - 10$

$2x = 18$

Therefore,

$x = rac{18}{2} = 9$

Emma's hourly rate of pay is €9.

Step 2

One week, she works for h hours and makes d deliveries. Write a formula in h and d for the wage (w) she receives.

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Answer

To formulate her wage based on hours worked and deliveries made, we have:

Earnings from hours worked: $9h$
Earnings from deliveries: $2d$

Thus, the total wage is:

$w = 9h + 2d$

Step 3

Another week, she works for 6 hours and makes 12 deliveries. She also works 5 hours on a Sunday, at time and a half, and makes some deliveries. In total, she receives €161.50 for that week. Find how many deliveries she makes on the Sunday.

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Answer

First, let's break down Emma's earnings for the week:

From 6 hours and 12 deliveries on the regular days:

-* Earnings from 6 hours = $9 imes 6 = 54$ -* Earnings from 12 deliveries = $2 imes 12 = 24$
Therefore, total earnings from the regular days:

$54 + 24 = 78$

Now considering the Sunday hours:
She works 5 hours at time and a half, which means:

$1.5 imes 9 imes 5 = 67.5$

Thus, the total earnings for that week is:

$78 + 67.5 + 2d = 161.50$

Simplifying gives:

$145.5 + 2d = 161.50$

Hence,

$2d = 161.50 - 145.5 = 16$

Therefore,

$d = 8$

Thus, Emma makes 8 deliveries on Sunday.

Emma works part time after school at the local takeaway - Leaving Cert Mathematics - Question 1 - 2016

Worked Solution & Example Answer:Emma works part time after school at the local takeaway - Leaving Cert Mathematics - Question 1 - 2016

One day, she works for 2 hours, makes 5 deliveries and is paid a total of €28. Find her hourly rate of pay.

One week, she works for h hours and makes d deliveries. Write a formula in h and d for the wage (w) she receives.

Another week, she works for 6 hours and makes 12 deliveries. She also works 5 hours on a Sunday, at time and a half, and makes some deliveries. In total, she receives €161.50 for that week. Find how many deliveries she makes on the Sunday.

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