*Find the Number Satisfying the Given Conditions

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Discussion Overview

The discussion revolves around finding a two-digit number based on specific conditions: the sum of its digits equals 12, and the number is 13 times its tens digit. Participants explore different approaches to set up the problem and solve for the number.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that the number could be 39 based on the digits 3 and 9, but expresses uncertainty about how to set up the equations.
  • Another participant proposes letting A represent the tens digit and B the ones digit, leading to the equations A + B = 12 and B = 3A.
  • A subsequent reply confirms the values A = 3 and B = 9, indicating that the solution is straightforward.
  • A later response agrees that the problem is indeed simple, implying satisfaction with the solution process.

Areas of Agreement / Disagreement

Participants generally agree on the simplicity of the problem and the derived values for A and B, but there is no explicit consensus on the overall approach to setting up the problem.

Contextual Notes

Some participants express uncertainty about the initial setup of the equations, indicating potential limitations in understanding how to formulate the problem correctly.

Who May Find This Useful

This discussion may be useful for individuals interested in problem-solving techniques in mathematics, particularly in relation to digit-based puzzles and algebraic setups.

karush
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The sum of the digits of a two-digit number is $12$ The number is $13$ times the tens digit. Find the number

well from $3+9=12$ we can see that the number would be $39$ which is $3\times 13$

but again I had trouble knowing how to set this up

In that $10t+u=12$ how do you set up $13t=$

mahalo much...
 
Last edited by a moderator:
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I would let A be the ten's digit and B be the one's digit. We are then told:

(1) $\displaystyle A+B=12$

$\displaystyle 10A+B=13A$ or:

(2) $\displaystyle B=3A$

Now substitute for B into (1) using (2) to solve for A, then from (2) you will have B.

What number do you find?
 
does it really have to be this easy...

A=3 then B=9

Oh and yes, Honolulu is a very nice place to live, me 12 years +
 
Last edited:
Yes, it is just that easy! (Handshake)
 

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