Latest Athenahealth Aptitude Question SOLUTION: Find the number of solutions for 3x+4y=60, if x and y are positive integers.

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Find the number of solutions for 3x+4y=60, if x and y are positive integers.

Asked In Athenahealth Aashu (10 years ago)

Unsolved Read Solution (8)

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Read Solution (8) :

RAKESH  (10 years ago)

3x+4y=60
=>x=(60-4y)/3
as x and y are positive integers, put y=1,2,3,... & find x
y=3,x=16
y=6,x=12
y=9,x=8
y=12,x=4
(x,y)=(4,12),(8,9),(12,6),(16,3)
only 4 solution

Is this solution Helpfull? Yes (21) | No (1)  

Gladson  (10 years ago)

Totally 6 solutions....
Y=15 & X=0
Y=12 & X=4
Y=9 & X=8
Y=6 & X=12
Y=3 & X=16
Y=0 & X=20

Is this solution Helpfull? Yes (7) | No (7)  

upendra singh chahar  (10 years ago)

8 solutions. according to manoj 4 and then interchange the values of x and y.

Is this solution Helpfull? Yes (6) | No (18)  

kavya  (9 years ago)

the answers can x=12 and y=4,x=10 and y=7.5,x=8 and y=9

Is this solution Helpfull? Yes (1) | No   

manoj  (10 years ago)

(x,y)=(4,12) ,(8,9) ,(12,6) ,(16,3) ----------only four solutions

Is this solution Helpfull? Yes | No (1)  

venky  (9 years ago)

3x=60-4y

keep substituting values for y such that (60-4y) will be divisible by 3. This can be done by substituting y as multiples of 3 (0,3,6,9,12,etc...). but since its mentioned x,y are positive integers,
60-4y>=0
therefore
y>=15

so values of y = 0, 3, 6, 9, 12 and 15
corresponding values of x = 20,16, 12, 8, 4, 0

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suresh  (8 years ago)

Infinetly many solutions

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Kannan Mohan  (8 years ago)

ANS :
3x must generate values that would make RHS divisible by 4 . Hence x=0,4,8,12,16,20
Number of solutions = 6

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