the sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?.

Question

I'm in the 8th grade in advanced math and we are going over last years lessons, and I never fully understood how to make an equation, but I can solve them easily.

Answer 1

There is a Tens Digit T and a ONE's Digit O [ <--- that is a CAPITAL LETTER O, not zero]

T + O = 7 <--- the sum of these digits is 7

THe number, in and of itself is 10*T + O

When the digits increase, the number becomes 10*O + T and it is

9 bigger than the original number. So the equation is:

10*O + T = 10*T + O + 9

10*O - O = 10*T - T + 9 <--- puts all of the O on one side and T on the other

9*O = 9*T + 9 <--- combines like terms

O = T + 1 <--- divides everything by 9

Then O - T = 1

and O + T = 7 <--- previous equation in bold above

Adding these last two equations together:

2*O = 8

O = 4 ----> T = 3

So the number is 34

Note that all of this algebra is unnessary in this case and can be skipped...

There are only a few two digit numbers whose digits add up to 7.

The are shown in the following table:

number reversed digits difference

07 70 63

16 61 45

25 52 27

34 43 9

43 34 -9

52 25 -27

61 16 -45

70 07 -63

Reversing the digits in each one basically reverses the order of the list;

The answer is obviously 34 and 43. Notice that the differences decrease

by 18