SOLUTION: 3 number equal 91. one number is multiplied by 6, one number has 6 added to it and the third has 6 subtracted from it, the answers are all the same. What are the 3 numbers?

Question 946772: 3 number equal 91.
one number is multiplied by 6, one number has 6 added to it and the third has 6 subtracted from it, the answers are all the same.
What are the 3 numbers?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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