Question

The Sum of two rational numbers is 5/ If one number exceeds the other by 2/3, find the two numbers

Answer 1

Answer:

13 / 6  and  17 / 6.

Step-by-step explanation:

Let first number be a.

Given their sum is 5

Other number exceeds by 2 / 3

So other number = a + 2 / 3

According to question.

a + a + 2 / 3 = 5

2 a + 2 / 3 = 5

( 6 a + 2 ) / 3 = 5

6 a + 2 = 15

6 a = 15 -2

6 a = 13

a = 13 / 6

So first number = 13 / 6

Other number = 13 / 6 + 2 / 3

                       = ( 13 + 4 ) / 6 = 17 / 6

Verification:

Adding both number and check that sum is 5 or not.

13 / 6 + 17 / 6

( 13 + 17 ) 6

30 / 6

5

Hence verified.

Answer 2

• Sum of two rational number is 5.

» Let one rational number be M.

» And another rational number be N.

• A.T.Q.

=> M + N = 5

=> M = 5 - N ________ (eq 1)

______________________________

• . If one number exceeds the other by $\frac{2}{3}$

=> M = $\dfrac{2}{3}$ + N

=> M = $\dfrac{2\:+\:3N}{3}$

=> 3M = 2 + 3N

=> 3(5 - N) = 2 + 3N ____ [From (eq 1)]

=> 15 - 3N = 2 + 3N

=> 15 - 2 = 3N + 3N

=> 13 = 6N

=> N = $\dfrac{13}{6}$

• Put value of N in (eq 1)

=> M = 5 - $\dfrac{13}{6}$

=> M = $\dfrac{30\:-\:13}{6}$

=> M = $\dfrac{17}{6}$

______________________________

Two numbers are : $\dfrac{17}{6}$ and $\dfrac{13}{6}$

_________ [ANSWER]