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2 years ago

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the sum of the reversed number and the original number is 154. Find the original number, if the ones digit in it is 2 less than

the tens digit.

2 answers:

VladimirAG [237]2 years ago

7 0

Answer:

The number is 86

Step-by-step explanation:

Let the number be $xy$ , then the reverse is $yx$

The sum of the reversed number and the original number is 154,

$\implies (10x+y)+(10y+x)=154$

We simplify this to get:

$\implies 11x+11y=154$ ....eqn(1)

If the ones digit in it is 2 less than the tens digit, then

$y=x-2$ ....eqn(2)

Putt equation (2) in (1)

$\implies 11x+11(x-2)=154$

$\implies 11x+11x-22=154$

$\implies 11x+11x=154+22$

$\implies 22x=176$

$\implies x=8$

Put x=8 in the second equation:

$y=8-2=6$

The original number is 86

lidiya [134]2 years ago

4 0

The original number is 86

$\texttt{ }$

<h3>Further explanation</h3>

Simultaneous Linear Equations could be solved by using several methods such as :

<em>Elimination Method</em>
<em>Substitution Method</em>
<em>Graph Method</em>

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

$\texttt{ }$

<em>Let:</em>

<em>The original number = yx</em>

<em>The ones digit = x</em>

<em>The tens digit = y</em>

$\texttt{ }$

<em>The ones digit in it is 2 less than the tens digit.</em>

$\boxed {x = y - 2}$ <em>→ Equation 1</em>

$\texttt{ }$

<em>The sum of the reversed number and the original number is 154.</em>

$xy + yx = 154$

$(10x + y) + (10y + x) = 154$

$11x + 11y = 154$

$\boxed {x + y = 14}$ <em>→ Equation 2</em>

$\texttt{ }$

<em>Equation 1 ↔ Equation 2 :</em>

$x + y = 14$

$( y - 2 ) + y = 14$

$2y - 2 = 14$

$2y = 14 + 2$

$2y = 16$

$y = 16 \div 2$

$y = 8$

$x = y - 2$

$x = 8 - 2$

$x = 6$

$\texttt{ }$

<h2>Conclusion:</h2>

The original number is 86

$\texttt{ }$

<h3>Learn more</h3>

Perimeter of Rectangle : brainly.com/question/12826246
Elimination Method : brainly.com/question/11233927
Sum of The Ages : brainly.com/question/11240586

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations

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