Question 295158
Your answer is:


a = -11
b = 15
c = 21


Here's how:


You set a, b, c equal to your numbers.   a is the first, b is the second, c is the third.


Your equations are:


a + b + c = 25 (equation 1)
a + b = c - 17 (equation 2)
c = b + 6 (equation 3)


Substitute (b + 6) for c in equations 1 and 2 to get:


a + b + (b + 6) = 25 (equation 1.1)
a + b = (b + 6) - 17 (equation 2.1)


Simplify equation 1.1 as follows:


Equation 1.1 is equal to:
a + b + (b + 6) = 25
Remove parentheses to get:
a + b + b + 6 = 25
Combine like terms to get:
a + 2b + 6 = 25
Subtract 6 from both sides of the equation to get:
a + 2b = 19 (equation 1.2)


Simplify equation 2.1 as follows:


Equation 2.1 is equal to:
a + b = (b + 6) - 17
Remove parentheses to get:
a + b = b + 6 - 17
Subtract b from both sides of this equation to get:
a = 6 - 17
Combine like terms to get:
a = -11 (equation 2.2)


You now have the following equations:


a + 2b = 19 (equation 1.2)
a = -11 (equation 2.2)
c = b + 6 (equation 3)


Substitute -11 for a in equation 1.2 to get:

a + 2b = 19 becomes:
-11 + 2b = 19
Add 11 to both sides of this equation to get:
2b = 30
Divide both sides of this equation by 2 to get:
b = 15 (equation 1.3)


You now have:


b = 15 (equation 1.3)
a = -11 (equation 2.2)
c = b + 6 (equation 3)


Substitute 15 for b in equation 3 to get:


c = b + 6 becomes:
c = 15 + 6 which becomes:
c = 21 (equation 3.1)


You now have:


a = -11 (equation 2.2)
b = 15  (equation 1.3)
c = 21  (equation 3.1)


These should be your numbers.


You confirm by going through the original 3 equations using these numbers to see if they are true.


Equation 1:


a + b + c = 25 becomes -11 + 15 + 21 = 25 which becomes -11 + 36 = 25 which becomes 25 = 25 which is true.


Equation 2:


a + b = c - 17 becomes -11 + 15 = 21 - 17 which becomes 4 = 4 which is true.


Equation 3:


c = b + 6 becomes 21 = 15 + 6 which becomes 21 = 21 which is true.


All 3 original equations are true, so your numbers must be:


a = -11
b = 15
c = 21


The sum of the second 2 numbers is 15 + 21 = 36.


That's your answer.