Real-Life Math -- Solution
This is a three-part problem: we must find (1) Sheila's initial
annual salary; (2) the increase in weekly salary; and (3) the hourly increase
she is asking for.
(1) To find Sheila's initial annual salary, first
calculate her present annual salary. From that we can find her previous salary
(after the first raise), and from that the original salary.
At present,
Sheila earns $7.50 an hour and works a 40-hour workweek. There are 52 weeks
in a year, so:
$7.50/hour x 40 hours/week x 52 weeks/year
= $15,600 per year
Sheila's present annual salary is
$15,600 per year.
Sheila's present salary came after a raise of 3.5%
of her previous salary. Let's call the previous salary Sp. Then:
Sp
+ 3.5% of Sp = $15,600 Sp + (0.035)Sp = $15,600
Sp
= $15,600/1.035
Sp = $15,072.46
Sheila's
previous salary was $15,072.46 per year.
Now we repeat the same steps
to find her initial salary. Let's call the initial salary Si. Then:
Si
+ 3.5% of Si = $15,072.46 (1.035) Si = $15,072.46Si
= $15,072.46/1.035
Si = $14,562.76
So
Sheila's starting annual salary was $14,562.76.
(2) We can use
the initial salary to calculate the initial weekly rate and use that to find
the increase to her present weekly rate.
Sheila's starting salary was
$14,562.76 per year. Divide that figure by 52 weeks per year to determine
her initial weekly salary:
$14,682.12 / 52 = $280.05She
currently earns $7.50 per hour, and her weekly rate is:
$7.50
x 40 = $300
The difference between her current weekly rate
and initial weekly rate is:
$300 - $280.05 = $19.95Sheila's
weekly rate has increased by $19.95.
(3) To find the hourly
increase Sheila is asking for, we need to compare her present hourly rate
of $7.50 with the hourly rate she would receive for an annual salary of $20,000.
Divide
$20,000 by 52 weeks per year and then by 40 hours per week to find the desired
hourly rate:
$20,000 / 52 / 40 = $9.61 The
difference between the desired and current hourly rates is:
$9.61
- $7.50 = $2.11
Sheila is asking
for a raise of $2.11 per hour.
"You want to have a good working relationship
with your staff and you need to be tolerant and flexible," says Lorna Zahn.
She is an office manager for a telecommunications company.