SOLUTION: my ones d igit is 2 more than my tens digit and my hundreds is 1 less than my tens, the sum of my digits is 16, who am i?

Question 557835: my ones d igit is 2 more than my tens digit and my hundreds is 1 less than my tens, the sum of my digits is 16, who am i?

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let T represent the tens digit, O represent the ones digit, and H represent the hundreds digit.
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The ones digit (0) is 2 more than the tens digit (T). So we can write the equation:
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O = T + 2
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The hundreds digit (H) is 1 less than the tens digit (T). So we can also write the equation:
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H = T - 1
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You are told that the sum of the 3 digits equals 16. So you can add the hundreds digit (H) to the tens digit (T) and to the ones digit (O) and the total must equal 16. In equation form this becomes:
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H + T + O = 16
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But you can replace H by its equal of T - 1. And you can also replace O by its equal of T + 2. When you do that the equation above becomes:
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T - 1 + T + T + 2 = 16
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On the left side of the equation combine the three T terms to get + 3T. And combine the - 1 and the + 2 to get + 1. This makes the left side of the equation simplify to the left side shown below:
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+ 3T + 1 = 16
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Now get rid of the + 1 on the left side by subtracting + 1 from both sides and the result is:
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3T = 15
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Solve for T by dividing both sides by 3 and you get:
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T = 5
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Since you now know that T equals 5, you can find H (the hundreds digit) from the equation:
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H = T - 1
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Substitute 5 for T and you have:
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H = 5 - 1 = 4
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And also since you now know that T equals 5, you can find O (the ones digit) from the equation:
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O = T + 2
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Substitute 5 for T and you have:
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O = 5 + 2 = 7
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With H = 4, T = 5, and O = 7 you can now write the answer. The number you were to find is 457.
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I hope this helps you to understand how to work problems of this type.
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