Question

There are 6 gray keys for every 11 black keys. Also, the number of black keys is 2 less than twice the number of gray keys. Use your answer to part (b) to determine how many gray keys and how many black keys there are.

Answer 1

$\text{ Answer: There are }12\text{ gray keys.}\\\\\text{ there are }22\text{ black keys.}$

Explanation:

Since we have given that

There are 6 gray keys for every 11 black keys .

So, the ratio will be 6:11

Let the number of gray keys be 6x

Let the number of black keys be 11x

Now, according to question,

$11x=2\times 2x-2\\\\11x=12x-2\\\\11x-12x=-2\\\\-x=-2\\\\x=2$

so,

$\text{ there are }6x=6\times 2=12\text{ gray keys.}\\\\\text{ there are }11x=11\times 2=22\text{ black keys.}$