SOLUTION: The following is known about three numbers: Twice the largest number plus the second largest number plus three times the smallest number is 147. The sum of the second largest num

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Question 1115585: The following is known about three numbers: Twice the largest number plus the second largest
number plus three times the smallest number is 147. The sum of the second largest number and twice
the smallest number is 29 more than the largest number. The largest number is 15 less than twice
the second largest number. Find the three numbers.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let’s the largest number be x, the second largest number y, and the smallest number z
given:
Twice the largest number plus the second largest number plus three times the smallest number is 147.
2x%2By%2B3z=147.....eq.1
The sum of the second largest number and twice the smallest number is 29 more than the largest number.
y%2B2z=x%2B29.....eq.2
The largest number is 15 less than twice the second largest number.
x=2y-15.....eq.3
to find the three numbers, solve the system:
2x%2By%2B3z=147.....eq.1
y%2B2z=x%2B29.....eq.2
x=2y-15.....eq.3
----------------------------
2x%2By%2B3z=147.....eq.1...substitute x from eq.3
2%282y-15%29%2By%2B3z=147
4y-30%2By%2B3z=147
5y=147-3z%2B30
y=%28147-3z%2B30%29%2F5....eq.1a
substitute y from eq.1a and x from eq.3 in eq.2
%28147-3z%2B30%29%2F5%2B2z=2y-15%2B29.....eq.2
%28147-3z%2B30%29%2F5%2B2z=2%28147-3z%2B30%29%2F5-15%2B29....multiply by 5
147-3z%2B30%2B10z=2%28147-3z%2B30%29-75%2B145
177%2B7z=294-6z%2B60-75%2B145
177%2B7z=424-6z
6z%2B7z=424-177
13z=247
z=247%2F13
z=19
go to
y=%28147-3z%2B30%29%2F5....eq.1a , substitute z
y=%28147-3%2A19%2B30%29%2F5
y=%28147-57%2B30%29%2F5
y=120%2F5
y=24
go to
x=2y-15.....eq.3 substitute y
x=2%2A24-15
x=48-15
x=33
so, your numbers are: 33, 24, and 19