Equation with Answer/Explanation

[Guest]

The sum of 2 numbers is s, and their difference is d. Determine the numbers.

Answer provided with problem:

s + d / 2 and s - d / 2.

How did they obtain the answer ?

[Guest]

Please reply. Thanks.

[Guest]

Let's denote the two numbers by x and y.

We know that
x + y = s
x - y = d

From the second equation we get x = y + d
and replace x from the first equation
x + y = s
(y+d) + y = s
2y +d = s
2y = s - d
[tex]y = \frac{s - d}{2}[/tex]

Now we know y and x = y + d
[tex]x = \frac{s - d}{2} + d[/tex]
[tex]x = \frac{s - d}{2} + \frac{2d}{2}[/tex]
[tex]x = \frac{s - d + 2d}{2}[/tex]

[tex]x = \frac{s + d}{2}[/tex]

s and d are 2 numbers

[Guest]

x = s - d / 2 + 2d /2

I don't understand this step.

[Guest]

Surely a simple solution would be.....

Let the two numbers be x and y.

We know that
x + y = s ......eqn1
x - y = d ......eqn2

Add them gives 2x = s + d so x = (s + d) / 2

Subtract them gives 2y = s - d so y = (s - d) / 2

[Guest]

I understand that. Thanks.

x = s - d / 2 + 2d /2 Would you also explain how you obtained this step. It is the one I am not clear.

[Guest]

x = s - d / 2 + 2d /2 Would you also explain how you obtained this step. It is the one I am not clear.
This is not my post....but I can explain anyway...
The method used by the other poster was "substitution" .....which I think makes it more difficult, that is why I posted my solution.

The part you query is....
x = (s - d) / 2 + d

but we can write d as (d/2 + d/2) ......ie. half of d plus half of d gives 2 halves of d = (2 x d)/2 = 2d/2.....it is done because the other part is also divided by 2 so easier to work with the same common denominator
x =( s - d) / 2 + (d /2) + (d/2)
x = (s/2) -(d/2) + (d/2) + (d/2) ....OR..... x = (s/2) -(d/2) + (2d/2)
The minus and plus d/2 cancel and leaves d/2 ..... OR ..... 2d/2 - d/2 = d/2 and leaves d/2
x = (s/2) + (d/2)
Same as (s + d)/2
and follow a similar calc. for y

[Guest]

" and follow a similar calc. for y "

x + y = s (1)
x - y = d (2)

y = d - x

x + (d - x) = s

I am stuck already.

[Guest]

There is a solution for y in the earlier posting.........

How you get there depends on how you manipulate the algebra.

Another way to look at it is.............
x + y = s ....so...... y = s - x
x - y = d .....so .....y = x - d
that means these both are equal....

s - x = x - d
s + d = 2x
x = (s + d) / 2

OR.......
x + y = s ....so...... x = s - y
x - y = d .....so .....x = d + y
that means these both are equal....
s - y = d + y
s - d = 2y
y = (s - d) / 2


What you seem to be doing wrong.....????????????????

" and follow a similar calc. for y " ....I had not noticed there was a calc for y earlier in the post.....

x + y = s (1)
x - y = d (2)

y = d - x .........watch the signs ....it should be -y = d - x OR y = x - d.......xxxxxxxxxxx

then it becomes x + x - d = s
and this gives 2x = s + d
So............. x = (s + d) / 2

which is the same as before.........

To calc for y................which I think you wanted to do......

x = y + d from (2)

then subs in (1) ......y + d + y = s

So..... 2y = s - d

gives........y = (s - d) / 2 as before

[Guest]

I understand now. Thanks again.