The sum of the digits of a three digit number is 15. If the tens digits and the hundreds digit are interchanged, the number is increased by 360. If the units digit is 1/4 of the sum of the hundreds and the tens digit, what is the number?
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Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. – José Carlos Santos May 04 '18 at 06:30
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2HINT: It is just a system of three linear equations with three variables. Just translate each of the clues into a corresponding equation. – TStancek May 04 '18 at 06:39
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As mentioned in the comments, you have a system of linear equations in three variables: $$a+b+c=15\\ 100 a+10 b+c+360=10 a+100 b+c\\ c=\frac{a+b}{4} $$
Simplifying you get $$a+b+c=15\\a+4=b\\a+b=4 c$$ You can work your way from here. $$\{\{a\to 4,b\to 8,c\to 3\}\}$$
John Glenn
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