SOLUTION: find four consescutive odd integers if the product of the two smaller integers is 112 less than product of the two larger integers.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: find four consescutive odd integers if the product of the two smaller integers is 112 less than product of the two larger integers.      Log On


   

Question 33398: find four consescutive odd integers if the product of the two smaller integers is 112 less than product of the two larger integers.
Answer by mszlmb(115) About Me  (Show Source):
You can put this solution on YOUR website!
SWEET a challenge!
ok so 4 consecutive odd integers whence A*B=C*D-112 and A < B < C < D. let's c..
D=C+2=B+4=A+6 (cuz they're all odd and consecutive)
therefore (by substitution)
(D-6)*(D-4)=(D-2)*(D)-112 ..cool!
move a couple things from here to there and
((D-6)*(D-4))-((D-2)*(D))=-112
so far %28D%5E2-10D%2B24%29-%28D%5E2-2D%29=-112 subtract them and u get
-8D+24=112 simple algebra from here..
minus 24 on both sides: -8D=-112-24 .: -8D=-136 divide both sides by -8 and D=17.
well if D=17, C=15, B=13, and A=11
let's check: 17*15= 17*3*5= 51*5= 255 and 13*11=143. 255-143=112
:)))
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