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The sum of two numbers is 100, their difference is 56, what are the two numbers?

User Bao Dinh
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2 Answers

3 votes

Answer: X = 78 and Y = 22.

Explanation:

Let's call the two numbers X and Y. We are given two pieces of information:

1. The sum of the two numbers is 100, so we can write this as an equation: X + Y = 100.

2. The difference between the two numbers is 56, which can also be written as an equation: X - Y = 56.

Now, you have a system of two equations with two variables:

1. X + Y = 100

2. X - Y = 56

You can solve this system of equations by adding the two equations together to eliminate the Y variable:

(X + Y) + (X - Y) = 100 + 56

This simplifies to:

2X = 156

Now, divide both sides by 2 to solve for X:

2X / 2 = 156 / 2

X = 78

Now that you know the value of X, you can substitute it into one of the original equations to find the value of Y. Let's use the first equation:

X + Y = 100

78 + Y = 100

Subtract 78 from both sides:

Y = 100 - 78

Y = 22

So, the two numbers are X = 78 and Y = 22.

User Ngruson
by
9.3k points
1 vote


\large\bf{\underline{\underline{\mathfrak{Question}:}}}

The sum of two numbers is 100, their difference is 56, what are the two numbers?


\large\bf{\underline{\underline{\mathfrak{Solution}:}}}

Let's assume that,


:{\Longrightarrow{\small{\rm{The\:one\:number\:=a}}}}


:{\Longrightarrow{\small{\rm{The\:other\:number\:=b}}}}

Now, according to the question,


:{\Longrightarrow{\small{\rm{a+b=100\:\:....(i)}}}}


:{\Longrightarrow{\small{\rm{a-b=56\:\:....(ii)}}}}

Here, substitution method must be applied.

Now, use the first equation


:{\Longrightarrow{\small{\rm{a+b=100}}}}


:{\Longrightarrow{\small{\rm{a=100-b}\:\:....(iii)}}}

Put the value of equation (iii) in equation (ii)


:{\Longrightarrow{\small{\rm{a-b=56}}}}


:{\Longrightarrow{\small{\rm{100-b-b=56}}}}


:{\Longrightarrow{\small{\rm{100-2b=56}}}}


:{\Longrightarrow{\small{\rm{2b=56-100}}}}


:{\Longrightarrow{\small{\rm{2b=-44}}}}


:{\Longrightarrow{\small{\rm{b=(-44)/(-2)}}}}


:{\Longrightarrow{\small{\rm{b=\frac{\cancel{-44}}{\cancel{-2}}}}}}


:{\Longrightarrow{\small{\rm{b=(22)/(1)}}}}


{\therefore{\small{\rm{b=22}}}}

Now, put this value in equation (iii) for getting the answer.


:{\Longrightarrow{\small{\rm{a=100-22}}}}


{\therefore{\small{\rm{a=78}}}}

For verification:

Put the value of a and b in the equation (i) and (ii)

We have,


:{\Longrightarrow{\small{\rm{a=78}}}}


:{\Longrightarrow{\small{\rm{b=22}}}}

In case 1 :


:{\Longrightarrow{\small{\rm{78+22=100}}}}


:{\Longrightarrow{\small{\rm{100=100}}}}


:{\Longrightarrow{\small{\rm{L.H.S=R.H.S}}}}

In case 2 :


:{\Longrightarrow{\small{\rm{78-22=56}}}}


:{\Longrightarrow{\small{\rm{56=56}}}}


:{\Longrightarrow{\small{\rm{L.H.S=R.H.S}}}}

Hence, verified!

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