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We're going to turn this into an equation and then use a little algebra to solve this problem. Your problem can be written like this:

x/12 + x/20 = 31

If you take a look at the equation, you'll see that x is equal to the number you're looking for. x/12 is the same as 1/12 times x or one twelfth of x. x/20 is the same way. Now we simply solve for x in this equation

x/12 + x/20 = 31

x + 12x/20 = 372 (i multiplied everything by 12)

20x + 12x = 7440 (now i multiplied everything by 20)

32x = 7440 (you can combine the two x values)

x = 232.5 (i divided by 32)

Now we check our answer:

232.5/12 = 19.375

232.5/20 = 11.625

19.375 + 11.625 = 31

It checks out.

So your answer is 232.5 or 465/2.

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Q: The sum of one twelfth and one twentieth parts is 31?
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