The sum of three numbers is 24. The third is 11 less than 2 times the second. 9 times the first is 7 more than 2 times the second. Find the numbers.

Answer 1

F + S + T = 24 F= 1st number, S = 2nd, T = 3rd

T = 2S - 11

9F = 7 + 2S

divide by 9

F + (7+2S)/9

substitute for F and T

(7+2S)/9 + S + 2S -11 = 24

7+2S + 9S + 18S - 99 = 216

29S = 216 + 99 - 7 = 308

S = 308/29 = the 2nd number

T = 2S -11 = 616/29 -11 = 616/29 - 319/29 = 297/29 = 3rd number

F = (7+2S)/9 = (7 +616/29)/9 = 819/261 = 1st number

the 3 numbers are 819/261, 308/29 and 297/29

they sum to 819/261 + 308/29 + 297/29 = about 3.14 + 10.62 +10.24 = 24

F =( 7+2(10.62))/9 = (7+ 21.24)/9 = 28.24/9 = 314

S = 308/29 = 10.62

T = 2S-11 = 2(10.62) - 11 = 21.24-11 = 10.24

although odds are the problem may have been mis-copied or has a slight typo, with more integer type solutions in the corrected version. If the problem had an 8 instead of 9, (8F = 7+ 2S) then F=3.5, S=10.5, T = 10 as exact answers, not rounded off. 3.5+10.5+ 10 = 24