End total same as starting total

Question

Malcolm and Maddie are studying for an exam.  Maddie posed 24 review questions.  As motivation, Malcolm will receive 7 pennies for every correct answer and will lose 5 pennies for every incorrect answer.  At the end of the session, Malcolm's total was the same as his starting total.  How many questions did Malcolm answer correctly?

Answer 1

Hi Shareeka:

 

Like all "word" problems, you must try to put the information into expressions or equations prior to seeking a solution.  In this problem you're having to figure out the number of correct answers to a total of 24 questions.

 

This means that the total of the of wrong answers PLUS right answers must be 24.  Simply put r + w = 24 where r stands for right answers and w stands for wrong answers.

 

Now if Malcolm ends up with the same amount of money that he started with after ADDING 7 pennies for each right answer and SUBTRACTING 5 pennies for each wrong answer does this mean that 7*r LESS 5*w is zero?  If it does then even if Malcolm began with $25 he will have $25 afterwards!  So it really doesn't matter just how much he started with does it?

 

So now you have two equations and two unknowns and you should be able to solve for each.