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QuestionFind the two-digit number where the unit's digit is 6, and adding 18 swaps its digits. What is the number?

Studdy Solution

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+x10x +6 +18 =60 + x

STEP 5

implify the equation.
10x+24=60+x10x +24 =60 + x

STEP 6

Rearrange the equation to isolate x.
10x−x=60−2410x - x =60 -24

STEP 7

implify the equation to find the value of x.
9x=369x =36

STEP 8

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

STEP 9

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

STEP 10

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

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