What two numbers have a sum of 67 and a difference of 9?

Answer 1

So you are looking for 2 numbers, let's call them X and Y. They have to work out as follows:

X+Y=67 & X/Y=9

There are many numbers that can add up to make 67, so let's work backwards with the other equation:

X/Y=9 = X=9*Y

We know it has to be less than 67. However, for this to be true, the numbers have to be less than 67/9, or else they couldn't add together to make 67.

67/9=7.45

So Y must be less than 7.45. So if we take a random number, let's say 6 and sub it for Y it would end up like this:

X=9*6 (54)

Then check that with the equations:

54+6=60 (wrong)

54/6=9 (right)

So that doesn't work, it has to be bigger than 6. Try 6.5:

X=9*6.5 (58.5)

Then check that with the equations:

58.5+6.5=65 (wrong)

58.5/6.5=9 (right)

Close, one more try, 6.7:

X=9*6.7 (60.3)

Then check that with the equations:

60.3+6.7=67 (right)

60.3/6.7=9 (right)

So the answer ends up being: 6.7

There is a more arithmatic way of solving it, if you can follow along. Here goes:

X/Y=9

X+Y=67

Since X/Y=9 you can move the X over and turn it into:

Y=9*X

Since you now have an equation value for Y you can put both equations together to form 1:

X+(9*X)=67

You can further simplify the equation as follows:

9*X=67-X

Then:

X=(67-X)/9

That's the answer if you are just going for a simplified equation.