Exact Science - Problem of The Day - 30

30

A three-digit number begins with the number 4. If you move it to the end of the number, you get a number that is 3/4 of the original. Find the original three-digit number.

Answer

The original number is 432.

SOLUTIOn

Let a be the number of tens of the original number, and b the number of ones, then the original number itself is 400+10a+b, and the new number is 100a+10b+4 or 0.75(400+10a+b). Let's create and solve the equation:

100a+10b+4=0.75(400+10a+b)

100a+10b+4=300+7.5a+0.75b

100a-7.5a+10b-0.75b=300-4

92.5a+9.25b=296

9.25(10a+b)=296

10a+b=296:9.25

10a+b=32

Thus, the original number has 3 tens and 2 ones, and the number itself is 432.

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