Question

the difference between the two numbers is 8.If 2 is added to the bigger number the result will be three times to the smaller number. Find the numbers using one variable.

Answer 1

let one no. be x and other no. be y

according to the question
X-Y=8
X=Y+8 1
And
2+X=3Y
2+(Y+8)=3Y (Substituting the value from eq. 1)
2+Y+8=3Y
10+Y=3Y
10=2Y
Y=5

So,
putting the value of Y in eq. 1 we get

X=5+8
X=13

therefore,
the reqd. numbers are 5 and 13

Answer 2

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✬ Smaller Number = 5 ✬

✬ Larger Number = 13 ✬

Explanation:

Given:

Difference of two numbers is 8.

After adding 2 to bigger number the result will be 3 times the smaller number.

To Find:

What is the number?

Solution: Let the larger and smaller number be x and y respectively. Therefore,

➟ x – y = 8

➟ x = 8 + y.......(i)

A/q

After adding 2 to bigger number the result will be 3 times the smaller number.

${\rm }⟹ x + 2 = 3(y)$

${\rm }⟹ 8 + y + 2 = 3y$

${\rm }⟹ 10 + y = 3y$

${\rm }⟹ 10 = 3y – y$

${\rm }⟹ 10 = 2y$

${\rm }⟹ 10/2 = y$

${\rm }⟹ 5 = y$

So, the two numbers are

➮ Smaller number is y = 5

➮ Larger number is x = 8 + 5 = 13

[ Verification ]

Adding 2 to 13 then we will get result as 3 times of 5.

$\sf{13 + 2 = 3(5)}$

$\sf{15 = 15}$

$\large\bold{\texttt {Verified }}$