SOLUTION: A group of office workers had some prize money to distribute among themselves. When all but one took $9 each, the last person only received $5. When they all took $8 each, there wa

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Question 1191509: A group of office workers had some prize money to distribute among themselves. When all but one took $9 each, the last person only received $5. When they all took $8 each, there was $12 left over. How much had they won?
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
A group of office workers had some prize money to distribute among themselves.
When all but one took $9 each, the last person only received $5.
When they all took $8 each, there was $12 left over. How much had they won?
~~~~~~~~~~~~~~~~~~~ 

Let n be the number of workers.


We can express the total money in two different ways.


One way is      the total money = 9*(n-1) + 5

Another way is  the total money = 8*n + 12.


Since the total money is the same,


    9*(n-1) + 5 = 8n + 12


Simplify and find n


    9n - 9 + 5 = 8n + 12

    9n - 4 = 8n + 12

    9n - 8n = 12 + 4

       n    =   16.


So, there are 16 workers, and the total prize money is  8n+12 = 8*16 + 12 = 140 dollars.    ANSWER

Solved.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

P = total prize money in dollars
n = number of people
n-1 = all but one person

All but one took $9 each, so we have (n-1)*9 = 9n-9 dollars taken.
The amount of money left over is P-(9n-9) = P-9n+9 which is set equal to the stated $5

P-9n+9 = 5
P = 5+9n-9
P = 9n-4

In the second scenario, all n workers took $8 each.
They took a total of 8n dollars.
There is $12 left over, so,
P - 8n = 12

Now apply substitution
P - 8n = 12
9n-4 - 8n = 12
n-4 = 12
n = 12+4
n = 16
There are 16 office workers total.
If all but one (aka 15 people) take $9 each, then we have 15*9 = 135 dollars taken. Add on the leftover $5 to get to 135+5 = $140

Or you can compute P like this
P = 9n-4
P = 9*16-4
P = 144 - 4
P = 140

Yet another way is to do
P - 8n = 12
P = 8n+12
P = 8*16+12
P = 128+12
P = 140
Like with many topics in math, there are multiple routes to take.
Feel free to use your favorite.


Answer: 140 dollars
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