Question

If 5a+3b=35 and a/b=2/5 , what is the value of a? A 14/5 B 7/2 C 5 D 7

Answer 1

`\sf\\A.\ 14/5`

Step-by-step explanation:

`\bold{Method\ 1:}`

`\sf\\5a+3b=35................(1)\\\\(a)/(b)=(2)/(5)\\\textsf{or, }5a=2b.............(2)\\\\\textsf{Substituting value of '5a' from equation (2) in equation (1),}\\2b+3b=35\\\textsf{or, }5b=35\\\textsf{or, }b=7\\\\\textsf{Equation(2) becomes}\\5a=2(7)=14\\\textsf{or, }a=14/5`

`\bold{Method\ 2:}`

`\sf\\\textsf{We have,}\\(a)/(b)=(2)/(5)\\\\\textsf{Let a = 2k and b = 5k}`

`\textsf{From the first equation,}\\\sf\\5a+3b=35\\\textsf{or, }5(2k)+3(5k)=35\\\textsf{or, }10k+15k=35\\\textsf{or, }25k=35\\\\\textsf{or, }k=(35)/(25)\\\\\textsf{or, }k=(7)/(5)`

`\textsf{Now,}\\\sf\\a=2k=2((7)/(5))=(14)/(5)`