Question

(x+1)/(2)=(y+2)/(3)=(x+y)/(4)

Please help, 50 points !!
I need to also show my work.

Answer 1

x = 5 and y = 7



x+1/2 = x+y/4 ...................... (1)
y+2/3 = x+y/4 ..................... (2)

From (1):
x+1/2 = x+y/4

4(x+1) = 2(x+y)

4x + 4 = 2x + 2y

4 = 2x + 2y - 4x

4 = -2x + 2y

2x - 2y = -4

2(x - y) = -4

x - y = -4/2

x - y = -2

x = y - 2 .................... (3)


From (2):
y+2/3 = x+y/4

4(y+2) = 3(x+y)

4y + 8 = 3x + 3y

4y - 3x - 3y = -8

-3x + y = -8 .................... (4)


Sub (3) into (4):
-3(y-2) + y = -8

-3y + 6 + y = -8

-2y = -8 - 6

-2y = -14

y = 7


Sub y = 7 into (3):
x = (7) - 2

x = 5