SOLUTION: The sum of three integers is 220. The sum of the first and second integers exceeds the third by 94. The third integer is 55 less than the first. Find the three integers.

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Question 1116881: The sum of three integers is 220. The sum of the first and second integers exceeds the third by 94. The third integer is 55 less than the first. Find the three integers.

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
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The sum of three integers is 220. The sum of the first and second integers exceeds the third by 94. The third integer is 55 less than the first.
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Three integers, x,y,z

system%28x%2By%2Bz=220%2Cx%2By-z=94%2Cz=x-55%29

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system%28x%2By%2Bz=220%2C%28x-z%29%2By=94%2C%28x-z%29=55%29
Look at the equation 2 and equation 3. They are equivalent to a single 55%2By=94.
This means highlight%28y=39%29; and you can probably deal with the rest.

Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x, y and z be the three integers, respectively.


Then first two parts of the condition gives you these two equations

x + y + z = 220,    (1)
x + y - z =  94.    (2)



Subtract eq(2) from eq(1). You will get

z - (-z) = 220 - 94 = 126  ====>  2z = 126  ====>  z = 126%2F2 = 63.



The third part of the condition says  z = x - 55.

It is equivalent to  x = z + 55,   or  x = 63 + 55 = 118.



Finally, from the equation (1),  y = 220 - x - z = 220 - 118 - 63 = 39.


Answer.  The three numbers are  118,  39  and  63.


Check.   Check it on your own that all three conditions are satisfied.