Mathematics, 06.10.2021 14:00 angel2939

sum of the digits of a two digit number is 9. when we interchange the digits, it is found that the resulting new number is greater than the original number by 27 . what is the two digit number?

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Answer from: yourgirlnevaeh

Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

Given that,

Sum of the digits of a two digit number is 9

So, Let we assume that

$\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{digit \: at \: tens \: place \: be \: x} \\ \\ &\sf{digits \: at \: ones \: place \: be \: 9 - x} \end{cases}\end{gathered}\end{gathered}$

Thus,

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{number \: formed = 10 (9 - x) + x = 90 - 9x} \\ \\ &\sf{reverse \: number = 10x + 9 - x= 9x + 9} \end{cases}\end{gathered}\end{gathered}$

According to statement

When we interchange the digits, it is found that the resulting new number is greater than the original number by 27.

$\rm\implies \:9x + 9 - (90 - 9x) = 27$

$\rm\implies \:9x + 9 - 90 + 9x = 27$

$\rm\implies \:18x - 81 = 27$

$\rm\implies \:18x = 27 + 81$

$\rm\implies \:18x = 108$

$\rm\implies \:\boxed{\tt{ x = 6}}$

So,

$\begin{gathered}\begin{gathered}\bf\:\rm :\longmapsto\:\begin{cases} &\sf{digit \: at \: tens \: place \: be \: 6} \\ \\ &\sf{digits \: at \: ones \: place \: be \: 3} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{number \: formed = 90 - 9x = 90 - 54 = 36} \\ \\ &\sf{reverse \: number = 9x + 9 = 54 + 9 = 63} \end{cases}\end{gathered}\end{gathered}$

Thus, 2 digit number is 36

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Basic Concept Used :-

Writing System of Linear Equation from Word Problem.

1. Understand the problem.

Understand all the words used in stating the problem.

Understand what you are asked to find.

2. Translate the problem to an equation.

Assign a variable (or variables) to represent the unknown.

Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Answer from: Quest

need more info

step-by-step explanation:

Answer from: Quest

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

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sum of the digits of a two digit number is 9. when we interchange the digits, it is found that the r...