Question

1. a) complete the table for kevins work hours.

\

$$\begin{tabular}{|l|r|r|l|} \\hline \\textbf{day} & \\textbf{start time} & \\textbf{end time} & \\textbf{hours worked} \\\\ \\hline monday & 3:30 p.m. & 9:00 p.m. & \\\\ \\hline wednesday & 4:00 p.m. & 11:00 p.m. & \\\\ \\hline saturday & 12:30 a.m. & 5:00 p.m. & \\\\ \\hline sunday & 7:00 a.m. & 2:30 p.m. & \\\\ \\hline \\end{tabular}$$

b) kevin earns \\$9.25/h. how much will he be paid this week?

1. sophie works 35 h/week. she earns \\$8.15/h. how much will she earn:

a) in 1 week?
b) in 1 year?
c) in 1 month?

1. sandra earns \\$300/week. she receives a 5\\% increase in pay.

a) calculate sandras weekly pay after her increase.
b) calculate sandras new yearly pay.
c) calculate sandras new monthly pay.

1. the regular price of a video game is \\$68.99. it is on sale for 40\\% off.

a) how much is the discount on this item?
b) how much is the tax on this item?

Explanation:

🆕 New Concept Discovered: Calculating Elapsed Time and Earnings
Working with time intervals and converting hourly rates to weekly, monthly, and yearly pay.

Step 1: Calculate Kevin's work hours (Question 4a)

To find the hours worked each day, we calculate the time elapsed from the start time to the end time:

• Monday: From 3:30 p.m. to 9:00 p.m.

\[
9:00 - 3:30 = 5.5\text{ hours}
\]

• Wednesday: From 4:00 p.m. to 11:00 p.m.

\[
11:00 - 4:00 = 7\text{ hours}
\]

• Saturday: From 12:30 a.m. to 5:00 p.m.
• From 12:30 a.m. to 12:00 p.m. (noon) is 11.5 hours.
• From 12:00 p.m. to 5:00 p.m. is 5 hours.

\[
11.5 + 5 = 16.5\text{ hours}
\]

• Sunday: From 7:00 a.m. to 2:30 p.m.
• From 7:00 a.m. to 12:00 p.m. (noon) is 5 hours.
• From 12:00 p.m. to 2:30 p.m. is 2.5 hours.

\[
5 + 2.5 = 7.5\text{ hours}
\]

Total hours worked:
\[
5.5 + 7 + 16.5 + 7.5 = 36.5\text{ hours}
\]

Step 2: Calculate Kevin's weekly pay (Question 4b)

Kevin earns \( \$9.25/\text{h} \) and worked \( 36.5\text{ hours} \):
\[
36.5 \times 9.25 = 337.625 \approx \$337.63
\]

Step 3: Calculate Sophie's earnings (Question 5)

Sophie works \( 35\text{ h/week} \) at \( \$8.15/\text{h} \).

• a) In 1 week:

\[
35 \times 8.15 = \$285.25
\]

• b) In 1 year (assuming 52 weeks in a year):

\[
285.25 \times 52 = \$14,833.00
\]

• c) In 1 month (using the yearly earnings divided by 12 months):

\[
\frac{14,833.00}{12} \approx \$1,236.08
\]

Step 4: Calculate Sandra's pay after a 5% increase (Question 6)

Sandra currently earns \( \$300/\text{week} \).

• a) Weekly pay after increase:

\[
\text{Increase} = 300 \times 0.05 = \$15
\]
\[
\text{New weekly pay} = 300 + 15 = \$315.00
\]

• b) New yearly pay (52 weeks):

\[
315 \times 52 = \$16,380.00
\]

• c) New monthly pay (yearly pay divided by 12):

\[
\frac{16,380.00}{12} = \$1,365.00
\]

Step 5: Calculate discount on the video game (Question 7)

The regular price is \( \$68.99 \) with a \( 40\% \) discount.

• Discount amount:

\[
68.99 \times 0.40 = 27.596 \approx \$27.60
\]

Answer:

Question 4

• a) Hours Worked Table:
• Monday: 5.5 hours
• Wednesday: 7 hours
• Saturday: 16.5 hours
• Sunday: 7.5 hours
• b) Kevin's Weekly Pay: \$337.63

---

Question 5 (Sophie)

• a) In 1 week: \$285.25
• b) In 1 year: \$14,833.00
• c) In 1 month: \$1,236.08

---

Question 6 (Sandra)

• a) New weekly pay: \$315.00
• b) New yearly pay: \$16,380.00
• c) New monthly pay: \$1,365.00

---

Question 7 (Video Game)

• Discount amount: \$27.60