Question

Elena has 15 red roses and 20 white roses to arrange in bouquets what is the greatest amount of bouquet of flowers she can make to have equal amount of roses in each.
3 bouquets with 5 red roses and 10 white roses in each
4 bouquets with 3 red roses and 7 white roses in each
5 bouquets with 3 red roses and 4 white roses in each
5 bouquets with 10 red roses and 15 white roses in each

Answer 1

We only have so many roses, so by finding out how many are used by these bouquets, we can deduce which one is possible.
1. 3 bouquets with 5 red roses and 10 white roses in each
Since there are 3 bouquets, and there are equal amounts of roses in each bouquet, multiply these values by 3 for the total number of roses used.  
3*5 red roses=15 red roses
3*10 white roses=30 white roses
This is impossible, as we only have 20 white roses.  This is incorrect.

2. 4 bouquets with 3 red roses and 7 white roses in each
Repeat the same process as used above.
4*3 red roses=12 red roses
4*7 white roses=28 white roses
Once again, this is impossible, as we only have 20 white roses.  Still not right.

3. 5 bouquets with 3 red roses and 4 white roses in each
Repeat the same process
5*3 red roses=15 red roses
5*4 white roses=20 white roses
These are the exact limits we have, meaning this is possible to do.  This is the correct answer.

4. 5 bouquets with 10 red roses and 15 white roses in each
Just to make sure we have the right answer, lets do the same process here.
5*10 red roses=50 red roses
5*15 white roses=75 white roses
This is way over the amount of roses permitted, so this is also incorrect.

Therefore, the correct answer is 5 bouquets with 3 red roses and 4 white roses in each.  I hope this helps!