Question

the differences between two numbers is 8 if 2 is added to the bigger number the result will be 3 times the smaller number find the numbers​

Answer 1

Answer:

x=larger number; y=smaller number

.

x-y=8

x=y+8                       Use this to substitute for x.

.

x+2=3y                     Substitute for x from above.

(y+8)+2=3y

y+10=3y                    Subtract y from each side.

10=2y                       Divide each side by 2.

 

5=y ANSWER 1: the smaller number is 5.

x=y+8  .=5+8=13   ANSWER 2: The larger number is 13.

CHECK:

x+2=3y

13+2=3(5)

15=15  

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.

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

$\sf{15 = 15}$

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