Question

A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. Find this number

Answer 1

Say the two- digit number has tens-digit as m
and the ones-digit as n

So the value of the number is 10m+n

Answer 2

we are given in the first sentence that the product of m and n is 8

Answer 3

this means when you multiply m and n you get 8

Answer 4

mn=8 is one equation that is given

Answer 5

no if we interchange m and n
what is the value of the new number?

Answer 6

A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. Find this number ...

At first, just as you can record 45 as 4•10+5, you can record a number ab (where a and b are digits), as a•10+b. THis will make it easier.

Then the sentences could be respectively translated as follows:
\(\color{#000000}{ \displaystyle a\cdot b=8 }\)
\(\color{#000000}{ \displaystyle (10a+b)+18=10b+a }\)

Answer 7

No you have a fairly simple system of equations to solve.