Rachelpaw wrote:

Sentence : The sum of Richard's age and Cindy's age in years is 17 more than the amount by which Tim's age is greater than Kathy's age.

Translation : R + C = (T - K) + 17

I don't understand (T-K) part.

How 'Tim's age is greater than Kathy's age' can translate '(T-K)'.

Isn't it T > K ?

Lets break it down, starting with the back half of the question:

"Tim's age is greater than Kathy's age."

So we know right away, T > K.

Next we can look at this part:

"is 17 more than the amount by which"

The "amount" is referring to the difference between T and K, which will be a positive number since Tim is older according to last part of the statement. That gives us T-K, (or |K-T| to cover all bases) which are the only options that produce a positive number

Once we know this, we can just plug in the 17+ and solve for the final equation