SOLUTION: whats the consecutive odd numbers such that the sum of the first and the second is 31 less than 3 times the third?

Question 944391: whats the consecutive odd numbers such that the sum of the first and the second is 31 less than 3 times the third?
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
F, S, and T are First, Second, and Third consecutive numbers.
S=F+2; T=F+4
F+S=3T-31 Substitute for S and T, solve for F
F+F+2=3(F+4)-31
2F+2=3F+12-31
2F+2=3F-19 Add 19 to each side
2F+21=3F Subtract 2F from each side
21=F ANSWER first number is 21.
S=F+2=21+2=23 ANSWER Second number is 23.
T=F+4=21+4=25 ANSWER Third number is 25.
CHECK
Sum of first and second is 31 less than 3 times third.
F+S=3T-31
21+23=3(25)-31
44=75-31
44=44
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