Question

Find two numbers if their ratio is 9:11 and their difference is 6. not 27 or 33 or -27 or -33

Answer 1

-27 and -33.

Explanation:

If the number have 9:11 of ratio, this can be expressed like this:
`(x)/(y) =(9)/(11)`. Because a ratio represents a equivalence between two fractions.

The problem says that their difference is 6, which can be expressed like:
`x-y=6`

Where x and y are the unknown numbers.

So:
`x=6+y`; we replace this equation in the ratios one.

`(x)/(y) =(9)/(11) \\(6+y)/(y) =(9)/(11) \\66+11y=9y\\66=9y-11y\\66=-2y\\(66)/(-2)=y\\ y= -33.`

To calculate the second number we use:
`x-y=6\\x=6+y\\x=6+(-33)\\x=6-33\\x=-27`

Hence, the two numbers that fit with the 9:11 ratio and their difference of 6 are -33 and -27.