Paul, Brian, and Philip each received a portion of a 208 prize. Brian received 4/8 less than Paul. Philip received 37 more than Paul. How much money did Brian receive?
To find out how much money Brian received, we need to first determine Paul's share.
Let's represent Paul's share as "x".
We know that Brian received 4/8 (which can be simplified to 1/2) less than Paul, so Brian's share can be represented as "x - 1/2x" or "1/2x".
Philip received 37 more than Paul, so his share can be represented as "x + 37".
The total prize money is given as 208, so we can write the equation:
x + (x - 1/2x) + (x + 37) = 208
Now, let's solve the equation to find Paul's share (x):
Combining like terms:
2x - 1/2x + 37 = 208
Multiplying the entire equation by 2 to eliminate the fraction:
4x - x + 74 = 416
Simplifying further:
3x + 74 = 416
Subtracting 74 from both sides:
3x = 342
Dividing both sides by 3:
x = 114
So, Paul's share is 114.
Now, let's calculate Brian's share (1/2x):
1/2 * 114 = 57
Therefore, Brian received 57 units of currency.