Math Math?

Question

The average salary of 5 employees at Toys 4 All is $35,000, but the average of these 5 employee's and their manager's salary is $41,000. Based on this information:

How much does the manager earn each year?

What is the total cost for Toys 4 All to raise the salaries of the 4 employees to $40,500?

Toys 4 All increased the manager’s salary to $80,000. How does this new change affect the mean salary of the 6 people (1 manger and 5 employees)?

Answer 1

Call the manager's salary x, and the total sum of the 5 employee's salary S. Then, we are given that:

S / 5 = 35000 and

(S + x) / 6 = 41000.

From the first equation we get S = 175000. Put this into the second equation and solve for x:

(105000 + x) / 6 = 41000

=>

175000 + x = 246000

=>

x = 71000 (I wish I was making that much!).

Now for the second part, we are given a new value of x (namely, 80000). What a raise!

So we are told to calculate (S + x) / 6 again:

(175000 + 80000) / 6 = 42500.

Answer 2

[ Considering that all the average salaries given are per annum/year basis]


Average salary of 5 employees = $35,000
Total salary of 5 employees = $35,000 X 5 = $1,75,000

Average salary of 5 emploees and the manager = $41,000
Total salary of 5 emploees and the manager = $41,000 X 6
= $2,46,000

Salary of the manager per year
= $2,46,000 - $1,75,000
= $71,000

Total cost for Toys 4 All to raise the salaries of 4 employees
=($40,500 X 4) + ($35,000 X 1) + $71,000
=$2,68,000

After increasing the salary of the manager,
total salary of the 6 people = ($35,000 X 5) + $80,000
= $2,55,000
So, average salary of the 6 people = $2,55,000/6
= $42,500

So, this new change affected the previous mean salary to increase by ($42,500 - $41,000) or $1,500

Answer 3

Let x = salary of manager.

Equation:
(5[$35,000] + x) / 6 = $41,000
$175,000 + x = $41,000 * 6
x = $246,000 - $175,000
x = $71,000

Answer: manager's salary is $71,000

Cost for Toys 4 All to raise the salaries of the 4 employees:
= 4($40,500 - $35,000)
= 4($5,500)
= $22,000

Answer: $22,000

Mean salary of 6 people after the manager's increase:
= ($80,000 - $71,000) / 6
= $9,000 / 6
= $1,500

Another way:
= ([$80,000 + 5{$35,000}] - 6[$41,000]) / 6
= ([$80,000 + $175,000] - $246,000) / 6
= ($255,000 - $246,000) / 6
= $9,000 / 6
= $1,500

Answer: The mean salary of 6 people will increase by $1,500.

Answer 4

The manager makes $71,000 a year.

I must point out an inconsistency 2 statement read 5 employees and their manager one statement reads 4 employees.