Lesson Solving entertainment problems on shortage of money

Solving entertainment problems on shortage of money

Problem 1

Let x represents the cost of one sundae in dollars.  Andrew is $2 short, so he has (x-2) dollars.  
Likewise, Michael has  (x-1) dollars.  Since together they have exactly enough to buy one sundae, x dollars, we can write:


    (x-2) + (x-1) = x.


Solve it for x

    2x - 3 = x,

    2x - x = 3,

       x   = 3.


ANSWER.  Each sundae costs 3 dollars.

Problem 2

Let x represents the cost of one sundae in dollars.  Lola is $4 short, so she must have (x-4) dollars.  
Likewise, Michael has  (x-3) dollars and Joaquin has (x-1).  Since together they have exactly enough to buy one sundae, x dollars, we can write:


  (x-4) + (x-3) + (x-1) = x.


Solve it for x



    3x - 8 = x

    3x - x = 8

       2x  = 8

        x  = 8/2 = 4.


ANSWER.  Each sundae costs 4 dollars.

Problem 3

In accordance with the context of the problem, all the shirts have the same price.


Let x be the price for one shirt.


Then Mr. Lee has, from one part of the condition,  3x + 6 dollars;

                  from the other part of the condition, he has  5x - 10 dollars.


It gives you THIS EQUATION


    3x + 6 = 5x - 10.


Simplify and find x


    6 + 10 = 5x - 3x

    16     = 2x

     x     = 16/2 = 8 dollars.


One shirt costs 8 dollars.


Hence, Mr Lee has  3x + 6 = 3*8 + 6 = 30 dollars.    ANSWER

Problem 4

Let x be the price of the gift, in dollars.


Since Bob is 20 dollars short, he has  x-20 dollars;  

similarly, John has x-34 dollars.


Altogether, they have  (x-20) + (x-34) = 2x-54.


It is exactly x-4 dollars (since altogether they are 4 dollars short)

    2x- 54 = x - 4.


From this equation,

    x = 54 - 4 = 50.



ANSWER.  The gift costs 50 dollars.

Problem 5

Let n be the number of workers.


We can express the total money in two different ways.


One way is      the total money = 9*(n-1) + 5

Another way is  the total money = 8*n + 12.


Since the total money is the same,


    9*(n-1) + 5 = 8n + 12


Simplify and find n


    9n - 9 + 5 = 8n + 12

    9n - 4 = 8n + 12

    9n - 8n = 12 + 4

       n    =   16.


So, there are 16 workers, and the total prize money is  8n+12 = 8*16 + 12 = 140 dollars.    ANSWER