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[lovehopefaith98]

I need some help figuring this problem out:

The result of dividing a two digit number by the number with its digits reversed is 7/4. If the sum of the digits is 12, what is the number?

I have no idea how to even begin, so any help is appreciated!

 

[wjm11]

The result of dividing a two digit number by the number with its digits reversed is 7/4. If the sum of the digits is 12, what is the number?

If our two digit number is "ab", that means that "a" is in the tens position and "b" is in the units positon, so ab = (10)(a) + b. For example, 36 = (3)(10) + 6. Make sense?

Can you proceed from here?

 

[lovehopefaith98]

Thanks! So from there, wouldn't I have to make another equation? How would I do that?

 

[soroban]

Hello, lovehopefaith98!

The result of dividing a two-digit number by the number with its digits reversed is 7/4.
If the sum of the digits is 12, what is the number?

Let \(\displaystyle t\) = tens digit.
Let \(\displaystyle u\) = units digit.

Then the number is: \(\displaystyle 10t + u\) . (This is what wjm11 explained.)

Then its reversal is: \(\displaystyle 10u + t\)

We are told: .\(\displaystyle \dfrac{10t+u}{10u+t} \:=\:\dfrac{7}{4} \quad\Rightarrow\quad 40t + 4u \:=\:70u + 7t\)

. . . . . . . . .\(\displaystyle 33t - 66u \:=\:0 \quad\Rightarrow\quad t - 2u \:=\:0\) .[1]


We are also told: .\(\displaystyle t + u \:=\:12\) .[2]


Now solve the system of equations.