A math word problem that I don't know how to solve

Question

Five housemates (A, B, C, and D) agreed to share the expenses of a party equally. If A spent $42, B spent $10, C spent $26, and E spent 30$, who owes whom and how much to equal it out? (I'm not even sure how to go about solving this. and sadly it pops up on quizzes a lot for me)

Answer 1

First, I'll assume you meant "D" rather than "E."  (note; I make typos very often)

 

It is important to understand the problem, so re-read it and put it into your own words.  How's this:  Four people want to share expenses for a party (or a meal, etc.) and they each spent a given amount.  How can they even out expenses?

 

Now, assign variables.  If possible, assign a variable to the value the problem wants you to find.  Here,

   Let x=the equal amount each person should pay      (note: this is the average of all expenses)

 

The average of all expenses = (total of expenses) / (number of people), so:

    x = Average = (42 + 10 + 26 + 30) / 4

    x = Average = 108 / 4

    x = Average = 27

 

Now we may compare the amount each person spent to what they agreed to spend (the average):

                   actual         ( 27 - actual )              difference

      A              42               -15                     pay A $15

      B              10                17                     B pays $17 more

      C              26                 1                      C pays $1 more

      D              30               -3                      pay D $3

 

Now, just to check:  When C pays $17 and D pays $1, pay $15 to A and $3 to D.  That was $18 in and out.

 

Answer 2

Hi Destiny:

 

First there seem to be some mistakes in the problem.  A,B,C,D makes on 4 housemates, not 5.  And you are only given the spending of 4 housemates, the last one mistaknely called E instead of D.  So let us say you have 4 housemates only, A, B, C and E.

 

the first step is to calculate the total expenses of the 4 housemates.  Simply add how much each one spent.  I get a total of $108.  If they were to share this expense equally, each one should have contributed 108 / 4 = $27.00

 

Now put a basket on the table and ask each housemate who paid less than $27.00 to put the cash difference they owe in the basket.  For example, B only spent $10, so she owes $27.00 - $10.00 = $17.00 into the basket.  Similarly, C owes $1.00 to the basket, which now contains $18.00

 

Now housemates A and E overpaid for the party, and can collect their due from the basket.  A is owed $42 - $27 = $15, and E is owed the remained to $18, which is $30 - $27 = $3.00

 

In the end, the basket is empty and everybody is happy!

 

Hope this helps you.

 

  Jean-Michel

Answer 3

If they are to share equally, it appears to ask you to average.  You have the amount each spent.  So simply add up the four amounts spent, and divide by 4 (the number of housemates).  This will give you the average expense (what each agreed to pay).  Then, for each, A,B, etc., find the difference between the average and the amount they actually paid.

 

Thus: the total is $42 + $10 + $26 + $30 = $108

$108/4 = $27

A is owed $42-$27= $15

B owes $27-$10= $17

C owes $27-$26=$1

E is owed $30-27 = $3.

 

So B pays $17 and C pays $1 to A & E.  To find out how much each pays to A & E, total the amount paid ($18),  Sure enough, the amount A & E are owed also total $18.