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Question 1032221: The sum of three integers is 353. The sum of the first and second integers exceeds the third by 63. The third integer is 51 less than the first. Find the three integers.
Found 4 solutions by josgarithmetic, Cromlix, stanbon, MathTherapy:
Answer by josgarithmetic(39630)   (Show Source):
Answer by Cromlix(4381)  (Show Source):
You can put this solution on YOUR website! Hi there,
The sum of three integers is 353.
x + y + z = 353........(1)
The sum of the first and second
integers exceeds the third by 63.
x + y = z + 63
Reorganize
x + y - z = 63.........(2)
The third integer is 51 less than
the first.
z = x - 51.............(3)
...................
Using Equations(1)and(2)
x + y + z = 353.....(1)
x + y - z = 63......(2)
Add
2x + 2y = 416......(4)
...........
Using Equation (3)
z = x - 51
substitute (x - 51) for z
in Equation (1)
x + y + z = 353.......(1)
x + y + (x - 51) = 353
x + y + x = 353 + 51
2x + y = 404.....(5)
Using Equations (4) and (5)
2x + 2y = 416 .....(4)
2x + y = 404.......(5)
Subtract:
y = 12.
Substitute y = 12 into
Equation (4)
2x + 2y = 416....(4)
2x +2(12) = 416
2x + 24 = 416
2x = 416 - 24
2x = 392
x = 196
Substitute y = 12 and
x = 196 into Equation (1)
x + y + z = 353.....(1)
196 + 12 + z = 353
z = 353 - 208
z = 145
x = 196, y = 12 and z = 145.
Hope this helps :-)
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The sum of three integers is 353. The sum of the first and second integers exceeds the third by 63. The third integer is 51 less than the first. Find the three integers.
----------------
a + b + c = 353
a+b = c + 63
c = a-51
---------------------------
Modify to get one variable::
c = a-51
b = -a + (a-51) + 63 = 12
a = a
---------------
Substitute and solve for "a"::
a + 12 + a-51 = 353
-----------------------------
2a - 39 = 353
2a = 392
--------------------
a = 196
b = 12
c = 196-51 = 145
---------------------
Cheers,
Stan H.
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Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website!
The sum of three integers is 353. The sum of the first and second integers exceeds the third by 63. The third integer is 51 less than the first. Find the three integers.
Let 1st, 2nd and 3rd integers be F, S, and T, respectively
We then get: F + S + T = 353 --------- eq(i)
Also, F + S = T + 63______F + S - T = 63 ------- eq (ii)
And, T = F - 51 ---------- eq (iii)
2T = 290 ------ Subtracting eq (ii) from eq (i)
T, or 3rd integer =  , or 
145 = F - 51 ------ Substituting 145 for T in eq (iii)
145 + 51 = F
F, or 1st integer = 
196 + S + 145 = 353 ----- Substituting 196 for F, nd 145 for T in eq (i)
341 + S = 353
S = 353 - 341
S, or 2nd integer = 
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