SOLUTION: A number equals the sum of two other numbers. The largest number diminished by 2 equals three times the smallest. The largest increased by 2 equals twice the result of diminishing

Question 171633: A number equals the sum of two other numbers. The largest number diminished by 2 equals three times the smallest. The largest increased by 2 equals twice the result of diminishing the middle number by 2. Find the numbers.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Three numbers a,b,c. a the largest, c the smallest
:
Write an equation for each statement arrange each in the standard form:
:
"A number equals the sum of two other numbers."
a = b + c
a - b - c = 0
;
"The largest number diminished by 2 equals three times the smallest."
a - 2 = 3c
a - 3c = 2
:
" The largest increased by 2 equals twice the result of diminishing the middle number by 2."
a + 2 = 2(b-2)
a + 2 = 2b - 4
a - 2b = -4 -2
a - 2b = -6
:
Arrange all three equations and add
a - b - c = 0
a +0b -3c = 2
a -2b +0c = -6
-----------------
3a - 3b - 4c = -4
;
From the 1st statement we know a = (b+c), substitute in the above equation
3(b+c) - 3b - 4c = -4
3b + 3c - 3b - 4c = -4
3b - 3b + 3c - 4c = -4
-c = -4
c = + 4
:
Find a, from the 2nd statement a - 2 = 3c, substitute 4 for c
a - 2 = 3(4)
a = 12 + 2
a = 14
:
Use the 1st statement to find b
14 = b + 4
b = 10
:
:
You can check these solutions in each statement
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