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
Question:

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.

Answers

Answer:The number is 86Step-by-step explanation:Let the number be  [tex]xy[/tex], then the reverse is [tex]yx[/tex]The sum of the reversed number and the original number is 154,[tex]\implies (10x+y)+(10y+x)=154[/tex]We simplify this to get:[tex]\implies 11x+11y=154[/tex]....eqn(1)If the ones digit in it is 2 less than the tens digit, then[tex]y=x-2[/tex]....eqn(2) Putt equation (2) in (1)[tex]\implies 11x+11(x-2)=154[/tex][tex]\implies 11x+11x-22=154[/tex][tex]\implies 11x+11x=154+22[/tex][tex]\implies 22x=176[/tex][tex]\implies x=8[/tex]Put x=8 in the second equation:[tex]y=8-2=6[/tex]The original number is 86

The original number is 86[tex]\texttt{ }[/tex]Further explanationSimultaneous Linear Equations could be solved by using several methods such as :Elimination MethodSubstitution MethodGraph MethodIf 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![tex]\texttt{ }[/tex]Let:The original number = yxThe ones digit = xThe tens digit = y[tex]\texttt{ }[/tex]The ones digit in it is 2 less than the tens digit.[tex]\boxed {x = y - 2}[/tex] → Equation 1[tex]\texttt{ }[/tex]The sum of the reversed number and the original number is 154.[tex]xy + yx = 154[/tex][tex](10x + y) + (10y + x) = 154[/tex][tex]11x + 11y = 154[/tex][tex]\boxed {x + y = 14}[/tex] → Equation 2[tex]\texttt{ }[/tex]Equation 1 ↔ Equation 2 :[tex]x + y = 14[/tex][tex]( y - 2 ) + y = 14[/tex][tex]2y - 2 = 14[/tex][tex]2y = 14 + 2[/tex][tex]2y = 16[/tex][tex]y = 16 \div 2[/tex][tex]y = 8[/tex][tex]x = y - 2[/tex][tex]x = 8 - 2[/tex][tex]x = 6[/tex][tex]\texttt{ }[/tex]Conclusion:The original number is 86[tex]\texttt{ }[/tex]Learn morePerimeter of Rectangle : https://brainly.com/question/12826246Elimination Method : https://brainly.com/question/11233927Sum of The Ages : https://brainly.com/question/11240586Answer detailsGrade: High SchoolSubject: MathematicsChapter: Simultaneous Linear EquationsKeywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations

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