Question 946772
your numbers are represented by x, y, and z.

you are given that 6x = y+6 = z-6


you are also given that x + y + z = 91


one way to solve this is to express all the variables in terms of one variable and then solve for that variable.


i'll express everything in terms of z.


6x = z-6 becomes x = (z-6)/6


y+6 = z-6 becomes y = z-12


after replacement, your eaution of x + y + z = 91 becomes (z-6)/6 + z-12 + z = 91


multiply both sides of this equation by 6 to get:


z-6 + 6z - 72 + 6z = 546


combine like terms to get 13z - 78 = 546


add 78 to both sides of this equation to get 13z = 624


divide both sides of this equation by 13 to get z = 48


since 6x = z-6, then 6x = 48-6 becomes 6x = 42 which becomes x = 7


since y+6 = z-6, then y+6 = 48-6 becomes y+6 = 42 which becomes y = 36


you get:


x = 7
y = 36
z = 48


x + y + z = 91 becomes 7 + 36 + 48 = 91 which becomes 91 = 91 which is true, confirming that the values of x, y and z are good.


6x = y+6 becomes 42 = 36+6 = 42 is also true.


6x = z-6 becomes 42 = 48-6 = 42 is also true.


36+6 = z-6 becomes 42 = 42 is also true.


all statements are true so the solution is good.