Math Snap

STEP 1

Assumptions1. The two-digit number has the digit6 in the unit's place.
. When18 is added to the number, the digits interchange their places.

STEP 2

Let's represent the two-digit number as10x +6, where x is the digit in the tens place.

STEP 3

According to the problem, when18 is added to the number, the digits change places. So, the new number becomes10*6 + x.

STEP 4

We can set up an equation based on the above information.
$$10x +6 +18 =60 + x$$

STEP 5

implify the equation.
$$10x +24 =60 + x$$

STEP 6

Rearrange the equation to isolate x.
$$10x - x =60 -24$$

STEP 7

implify the equation to find the value of x.
$$9x =36$$

STEP 8

olve for x.
$$x =36 / =4$$

STEP 9

Substitute x =4 into the original numberx +6 to find the two-digit number.
$$Number =*4 +6$$

Calculate the number.
$$Number =40 +6 =46$$The two-digit number is46.