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

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

It is 2 out of 8 she will pick green and 3 out of 7 she will pick green but red and green would be 5 out of 5 so 50% chance