SOLUTION: the sum of two numbers is 255. when the smaller number is subtracted from the larger, the result is -39.find the numbers

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Question 99863: the sum of two numbers is 255. when the smaller number is subtracted from the larger, the result is -39.find the numbers
Found 4 solutions by stanbon, jim_thompson5910, checkley71, doukungfoo:
Answer by stanbon(48568) About Me  (Show Source):
You can put this solution on YOUR website!
the sum of two numbers is 255. when the smaller number is subtracted from the larger, the result is -39.find the numbers
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x+y=255
x-y=-39
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Add the two equations to get:
2x = 216
x = 108
y = 147
================
Cheers,
Stan H.

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

1%2Ax%2B1%2Ay=255
1%2Ax-1%2Ay=-39

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.

Solve for y for the first equation

1%2Ay=255-1%2AxSubtract 1%2Ax from both sides

y=%28255-1%2Ax%29 Divide both sides by 1.


Which breaks down and reduces to



y=255-1%2Ax Now we've fully isolated y

Since y equals 255-1%2Ax we can substitute the expression 255-1%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


1%2Ax%2B-1%2Ahighlight%28%28255-1%2Ax%29%29=-39 Replace y with 255-1%2Ax. Since this eliminates y, we can now solve for x.

1%2Ax-1%2A%28255%29-1%28-1%29x=-39 Distribute -1 to 255-1%2Ax

1%2Ax-255%2B1%2Ax=-39 Multiply



1%2Ax-255%2B1%2Ax=-39 Reduce any fractions

1%2Ax%2B1%2Ax=-39%2B255Add 255 to both sides


1%2Ax%2B1%2Ax=216 Combine the terms on the right side



2%2Ax=216 Now combine the terms on the left side.


cross%28%281%2F2%29%282%2F1%29%29x=%28216%2F1%29%281%2F2%29 Multiply both sides by 1%2F2. This will cancel out 2%2F1 and isolate x

So when we multiply 216%2F1 and 1%2F2 (and simplify) we get



x=108 <---------------------------------One answer

Now that we know that x=108, lets substitute that in for x to solve for y

1%28108%29-1%2Ay=-39 Plug in x=108 into the 2nd equation

108-1%2Ay=-39 Multiply

-1%2Ay=-39-108Subtract 108 from both sides

-1%2Ay=-147 Combine the terms on the right side

cross%28%281%2F-1%29%28-1%29%29%2Ay=%28-147%2F1%29%281%2F-1%29 Multiply both sides by 1%2F-1. This will cancel out -1 on the left side.

y=-147%2F-1 Multiply the terms on the right side


y=147 Reduce


So this is the other answer


y=147<---------------------------------Other answer


So our solution is

x=108 and y=147

which can also look like

(108,147)

Notice if we graph the equations (if you need help with graphing, check out this solver)

1%2Ax%2B1%2Ay=255
1%2Ax-1%2Ay=-39

we get


%0D%0A++drawing%28+500%2C+600%2C+-118%2C+118%2C+-157%2C+157%2C%0D%0A++++graph%28+500%2C+600%2C+-118%2C+118%2C+-157%2C+157%2C+%28255-1%2Ax%29%2F1%2C+%28-39-1%2Ax%29%2F-1+%29%2C%0D%0A++++blue%28++circle%28+108%2C+147%2C+1.57333333333333+%29+%29+%0D%0A++%29%0D%0A++graph of 1%2Ax%2B1%2Ay=255 (red) and 1%2Ax-1%2Ay=-39 (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.


and we can see that the two equations intersect at (108,147). This verifies our answer.


-----------------------------------------------------------------------------------------------
Check:

Plug in (108,147) into the system of equations


Let x=108 and y=147. Now plug those values into the equation 1%2Ax%2B1%2Ay=255

1%2A%28108%29%2B1%2A%28147%29=255 Plug in x=108 and y=147


108%2B147=255 Multiply


255=255 Add


255=255 Reduce. Since this equation is true the solution works.


So the solution (108,147) satisfies 1%2Ax%2B1%2Ay=255



Let x=108 and y=147. Now plug those values into the equation 1%2Ax-1%2Ay=-39

1%2A%28108%29-1%2A%28147%29=-39 Plug in x=108 and y=147


108-147=-39 Multiply


-39=-39 Add


-39=-39 Reduce. Since this equation is true the solution works.


So the solution (108,147) satisfies 1%2Ax-1%2Ay=-39


Since the solution (108,147) satisfies the system of equations


1%2Ax%2B1%2Ay=255
1%2Ax-1%2Ay=-39


this verifies our answer.






So the two numbers are 108 and 147

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
X+Y=255 OR X=255-Y
Y-X=-39 NOW REPLACE X WITH (255-Y) & SOLVE FOR FOR Y
Y-(255-Y)=-39
Y-255+Y=-39
2Y=-39+255
2Y=216
Y=216/2
Y=108 ANSWER FOR THE LARGER NUMBER.
Y-108=255
X=255-108
X=147 FOR THE SMALLER NUMBER.
--------------------------------------------------------------------
THIS WORKS OUT MATHEMATICALLY BUT NOT LOGICALLY.
108 IS NOT A LARGER NUMBER THAN 147!!!!!!!!

Answer by doukungfoo(195) About Me  (Show Source):
You can put this solution on YOUR website!
First set some variables
Let the first number = x
Let the second number = y
Given: sum of two numbers is 255
so
x + y = 255
Given: the differenc of two numbers is -39
so
x - y = -39
Now set the fist equation equal to x
so
x + y = 255
x = 255 - y
Now replace the x in x - y = -39 with 255 - y
so
x - y = -39
255 - y - y = -39
255 - 2y = -39
-2y = -39 - 255
-2y = -294
%28-2y%29%2F-2+=+%28-294%29%2F-2
y = 147
Now we have found one of the numbers to be 147
Next we can use that to find the other number
so we know from the given that x + y = 255
replace y with 147 and solve for x
x + y = 255
x + 147 = 255
x = 108
Now we found the other number to be 108
So we x = 108 and y = 147
To check our results just plug the values for x and y into
x + y = 255
and
x - y = -39
so here we go
x + y =255
108 + 147 = 255
255 = 255
It works so lets try the other one
x - y = -39
108 - 147 = -39
-39 = -39
This works too. So we know that we have successfully solve the problem.