It is given that $ 5 \frac{3}{a} \times b \frac{1}{2}=19 $ (where the two fractions are mixed fractions); then find the value of $ a+b $.

Given :

$5\frac{3}{a}\times b\frac{1}{2}=19$

To find :

We have to find the value of $a+b$

Solution :

$ 5\frac{3}{a} \times b\frac{1}{2} $=19

$\frac{5\times a+3}{a} \times \frac{b\times 2+1}{2}=19$

$ ( 5a+3)( 2b+1) =19\times 2a$

$( 5a+3)( 2b+1) =38\times a$

This implies,

$5a+3=38$  \ or \ $ 5a+3=a$

$5a=38-3$ \ or \ $ 5a-a=-3$

$5a=35$ \ or \ $ 4a=-3$ 

$a=\frac{35}{5}  \ or \  a=\frac{-3}{4}$

 which is not correct a=7

Therefore, If $5a+3=38$ then $2b+1=a$

$2b+1=7$

$2b=7-1$

$2b=6$

$b=\frac{6}{2}$  $b=3$

The value of $ a+b \ is \ 7+3=10$  

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Updated on: 10-Oct-2022

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