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Marianna [84]
3 years ago
11

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.

Mathematics
2 answers:
VladimirAG [237]3 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]3 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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