Q: If 36 is split into two parts, and the sum of 8 times the first part and 3 times the second part is 203, what is the value of the first part?  

We can set up an equation to represent the given information:
8x + 3y = 203

where x represents the first part and y represents the second part. We know that the total of the two parts is 36, so we can add another equation to represent this:
x + y = 36

To solve for x, we can use elimination method by multiplying the second equation by 8 and subtracting it from the first equation:
8x + 3y - 8x - 8y = 203 - 288
-5y = -85
y = 17


We can substitute this value of y back into the second equation to solve for x:
x + 17 = 36
x = 36 - 17
= 19

Therefore, the first part is 19.