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, there was $12 left over. How much money had they won?

I keep getting $68 but the answer says $140. Can someone please help me. Thanks

let the number of workers be x

first case: amount of money = 9(x-1) + 5
2nd case: amount of money = 8x + 12

9(x-1) + 5 = 8x + 12
9x - 9 + 5 = 8x + 12
x = 16

amount of money = 9(15) + 5 OR 8(16) + 12 = $140

Ahhh thank you so much, I did 9x+5=8x+12, I didnt do x-1. Thanks for clearing this up for me.

Let's solve the problem step-by-step:

Let's assume that the total amount of prize money won by the group is represented by "X."

Step 1: When all but one took $9 each, the last person received $5.
In this scenario, all the office workers except the last one took $9 each. So the remaining money can be calculated as: (X - $9 * (n-1)), where "n" represents the total number of office workers.

According to the problem statement, the last person received $5, so we can write the equation as follows:
(X - $9 * (n-1)) + $5 = X

Step 2: When they all took $8, there was $12 left over.
In this scenario, all the office workers took $8 each. So the remaining money can be calculated as: (X - $8 * n).

According to the problem statement, there was $12 left over, so we can write the equation as follows:
(X - $8 * n) = $12

Now, we have two equations:
(X - $9 * (n-1)) + $5 = X ----> Eqn 1
(X - $8 * n) = $12 ----> Eqn 2

Let's solve these equations to find the value of X and n.

Expanding Eqn 1:
(X - $9n + $9 + $5 = X
X - $9n + $14 = X

Simplifying Eqn 1:
-$9n + $14 = 0
-$9n = -$14
n = -$14 / -9
n = 1.5555...

Since n represents the number of office workers, we need to have a whole number. Therefore, we round the value of n up to 2.

Putting the value of n = 2 in Eqn 1:
(X - $9 * (2-1)) + $5 = X
(X - $9 + $5 = X
X - $4 = X
-$4 = 0

This is not possible, so there seems to be an error in the calculations. Let's double-check the problem statement and attempt the calculations again.

To solve this problem, we can set up a system of equations. Let's denote the total prize money as "x" and the number of office workers as "n."

First, we know that when all but one took $9 each, the last person received $5. This means that (n-1) people took $9 each, and the remaining person received $5. So, we can write the equation:

9 * (n-1) + 5 = x

Next, we know that when they all took $8, there was $12 left over. This means that the total amount they took is $12 less than the total prize money:

8n + 12 = x

We now have a system of two equations:

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

To solve this system, we can substitute the second equation into the first equation:

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

Expanding and simplifying:

9n - 9 + 5 = 8n + 12
9n - 4 = 8n + 12

Rearranging the equation:

9n - 8n = 12 + 4
n = 16

Now that we know the value of "n" is 16, we can substitute it into either of the original equations to find the total prize money "x." Let's use the second equation:

8n + 12 = x
8 * 16 + 12 = x
128 + 12 = x
x = 140

Therefore, the total prize money the group had won was $140, not $68 as you initially calculated.