SOLUTION: Ben has won 20% more chess matches than Amy,while Amy has won 25% more chess matches than Mary Kay. By what percent does the number that Ben has won exceed the number that Mary Kay

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Ben has won 20% more chess matches than Amy,while Amy has won 25% more chess matches than Mary Kay. By what percent does the number that Ben has won exceed the number that Mary Kay      Log On


   

Question 289043: Ben has won 20% more chess matches than Amy,while Amy has won 25% more chess matches than Mary Kay. By what percent does the number that Ben has won exceed the number that Mary Kay has won?
(1) 40% (2) 45% (3) 50% (4) 55% (5) None of the above
Answer by Grinnell(63) About Me  (Show Source):
You can put this solution on YOUR website!
First we are dealing with percentages and their relationships.
We are not dealing with the actual 'number' of games.
When dealing with 'take a number' or 'only percentages'
it is ALWAYS the rule of thumb to use the number one hundred--100!!!!!!!!!
This keeps things simple.
Now watch this!....Why don't we let the number Mary Kay won be 100??
WE CAN DO THIS. N O W do you see how this gets simpler?
Now what is 25% of 100? 25! add this to 100 we get 125 games that Amy won.
Now what is 20% of 125? 25! Add this to 125 we get 150 games that Ben won.
NOW WE GO BACK TO SEE (AGAIN WHAT THE PROBLEM IS ASKING FOR)
The number Ben has won exceeds the number Mary Kay has won by 50 games.
50 games/100 games = a 50% increase. Ben has won 50% more games than Mary Kay has won.
50% is your answer!
Question: If you reduce 'a number' by 20%, what PERCENTAGE of the remaining number must be added
to the remaining number to get the ORIGINAL number? REMEMBER THE RULE OF THUMB!!!! Let the original number be 100. 20% of this is 80. WHAT % OF 80 MUST BE ADDED to 80 to get 100----25%!! {20/80=25%} REMEMBER TO TRY TO USE THE NUMBER 100 WHENEVER POSSIBLE.
'A NUMBER' HOLDS TRUE FOR ALL NUMBERS--WE JUST DECIDED TO CHOOSE 100--TO MAKE THINGS EASIER!!!!!