Question

PLEASE SOLVE

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 (E) 9

Answer 1

`a = (14)/(5)`

Explanation:

`5a + 3b = 35 \\ 3b = 35 - 5a \\ b = (35)/(3) - (5)/(3) a \\ put \: b\: = (35)/(3) - (5)/(3) a \: into \: (a)/(b) = (2)/(5) \\ (a)/( (35)/(3) - (5)/(3) a) = (2)/(5) \\ (a)/( (35 - 5a)/(3) ) = (2)/(5) \\ (3a)/(35 - 5a) = (2)/(5) \\ 5(3a) = 2(35 - 5a) \\ 15a = 70 - 10a \\ 15a + 10a = 70 \\ 25a = 70 \\ a = (70)/(25) \\ a = (14)/(5)`

Answer 2

14/5

Explanation:

So first i manipulated a/b= 2/5. i multiplied both sides by 5 making it 5a/b=2. Then i multiplied both sides by b making it 5a=2b. Then i substituted 2b into 5a+3b=35. Making it 2b+3b=35. then i simplified it making it 5b=35. Then i solved for b making it b=7. Then i substituted b into 5a+3b=35. So that it looked like this 5a+3*7=35. then it became 5a+21=35. Then you subtract 21 making it 5a=14. You then divide by 5 making it a=14/5