Question 124890:
there are four numbers. the first is twenty less the second, the third is one more than twice the first and the forth is four more than the third. we also know that the sum of the second equals the sum of the third and fourth numbers. find the numbers.
Found 2 solutions by stanbon, checkley71:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! there are four numbers.
the first is twenty less the second,
the third is one more than twice the first and
the forth is four more than the third.
the sum of the second and first equals the sum of the third and fourth numbers.
find the numbers.
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Let 1st,2nd,3rd,4th be a,b,c,d
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EQUATIONS:
a = b-20
c = 2a+1
d = c+4
b + a = c+d
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Rearrange the four equations:
a -b + 0 + 0 = -20
2a + 0 - c + 0 = -1
0 + 0 + c - d = -4
a + b - c - d = 0
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I used the matrix function of a TI calculator to get:
1st = 7
2nd = 27
3rd = 15
4th = 19
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Cheers,
Stan H.
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website! LET THE 3 NUMBERS BE W,X,Y,Z. WHERE:
W=X-20
X=Y+Z
Y=W+1
Z=Y+4
WHERE DO WE START TO ELIMINATE THESE UNKNOWNS?????
LETS START WITH THE W & X.
W=(Y+Z)-20 NOW REPLACE W BY(Y-1)
Y-1=Y+Z-20 NOW CANCEL OUT THE Y TERMS.
-1=Z-20 NOW REPLACE Z BY Y+4
-1=Y+4-20 NOW SOLVE FOR Y.
Y=-1-4+20
Y=15 ANSWER. NOW SOLVE FOR Z.
Z=15+4=19 ANSWER. NOW SOLVE FOR X.
X=15+19=34 ANSWER. NOW SOLVE FOR W.
W=34-20=14 ANSWER.
THUS WE HAVE:
W=14
X=34
Y=15
Z=19
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