SOLUTION: The sum of three numbers is 29. Twice the first number is eighteen more than three times the second number. The difference of the third and second numbers is one more than the firs

Question 851424: The sum of three numbers is 29. Twice the first number is eighteen more than three times the second number. The difference of the third and second numbers is one more than the first number. Find the numbers.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The sum of three numbers is 29.
Twice the first number is eighteen more than three times the second number.
The difference of the third and second numbers is one more than the first number.
Find the numbers.
:
Let the three number be a, b, c
Write an equation for each statemennt
:
"The sum of three numbers is 29."
a + b + c = 29
" Twice the first number is eighteen more than three times the second number."
2a = 3b + 18
a = b + 18/2
a = 1.5b + 9
" The difference of the third and second numbers is one more than the first number."
c - b = a + 1
Rearrange this, add to the 1st equation
-a - b + c = 1
a + b + c = 29
----------------adding eliminates a and b, find c
2c = 30
c = 15
:
Replace c in the 1st equation
a + b + 15 = 29
subtract 15 from both sides
a + b = 14
replace a with 1.5b+9
1.5b+9 + b = 14
2.5b = 14 - 9
2.5b = 5
b = 5/2.5
b = 2
:
Find a
a = 1.5(2) + 9
a = 3 + 9
a = 12
:
Find the numbers. 12, 2, 15 are the numbers
:
You can check this in the 2nd and 3rd statements
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