SOLUTION: Three numbers are such that the second is six less than three times the first, and the third is two more than two-thirds of the second. If the sum of the numbers is 172, find the s

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Question 603032: Three numbers are such that the second is six less than three times the first, and the third is two more than two-thirds of the second. If the sum of the numbers is 172, find the smallest number.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Three numbers: a, b, c
:
are such that the second is six less than three times the first,
b = 3a - 6
or
3a = b + 6
divide by 3
a = 1%2F3b + 2
:
and the third is two more than two-thirds of the second.
c = 2%2F3b + 2
:
If the sum of the numbers is 172,
a + b + c = 172
Replace a, and c
(1%2F3b + 2) + b + (2%2F3b + 2) = 172
Combine like terms
2b + 4 = 172
2b = 172 - 4
2b = 168
b = 168/2
b = 84 is the 2nd number
then
a = 1%2F3(84) + 2
a = 28 + 2
a = 30 is the 1st number
and
c = 2%2F3(84) + 2
c = 56 + 2
c = 58
:
Check: 30 + 84 + 58 = 172
:
find the smallest number. 30