Question

One number is 6 more than the other,if three times the sum of the two numbers is equal to 22 more than the larger number,what are the two numbers?

Answer 1

Let
`x,y [tex] be the two numbers. One number is 6 more than the other, so let's say that [tex] x = y+6 \iff y = x-6`

Also, three times the sum of the two number (i.e.
`3(x+y)`) is equal to 22 more than the larger number (i.e.
`22+x`). Note that
`x` is the largest, because it is 6 more than
`y`.

So, if we set the two expressions to be equal, and we substitute
`y = x-6`, we have

`3(x+y) = 22+x \iff 3(x+x-6) = 22+x \iff 3(2x-6) = 22+x \iff 6x-18=22+x \iff 5x = 40 \iff x=8`

And since
`x` is 6 more than
`y`, we have
`y=2`