Algebra and a Spy Story with a Briefcase for Solving Algebra Word Problems

I explained in my previous blog about algebra word problems being difficult without background information.  This blog will just give the problems and the equations.  The "spy"  (x) will be in red.  The second number, the spy's partner will be in blue. The briefcase they are searching for (the answer) will be in green.

   
 The sum of two numbers is twenty-four.  The larger number is three times the smaller   number.  Find the numbers.
                              x + 3x = 24



  One of two numbers is two-thirds the other number.  The sum of the numbers is 45.  Find the numbers.

                            x + 2 x = 45
                          3


  The difference of two numbers is 19.  The larger number is 3 more than twice the smaller.  Find the numbers. 

                      2x + 3 - x  = 19

(This one was more complicated, BUT remembering that there is always just an x and that this was a subtraction problem, you needed to work backwards from there).



  320 tickets were sold to the school play.  There were 3 times as many student tickets sold as adult tickets.  Find the number of each.

                      x + 3x = 320   (the spy is the adult tickets)

   


 The first number is eight more than the second number.  Three times the second number plus twice the first number is equal to 26.  Find the numbers. (Don't give up yet).
    Let's work through this:  x is the second number.  So we'll start with the first basic equation:  x + 8 + x = 26    Because we know who the identities of the spys, we can add on to this information.  The second part of this equation is:
               2(x+8) + 3x = 26  The briefcase didn't change. But we have to use the distributive power to solve this problem.  See "Lifeguard" blog.

Three times the second number (the spy) is added to twice the first number.  Because the first number is an entity, parentheses ARE NEEDED to multiply is by two. 
   The resulting simplification of the equation is:
              2x + 16 + 3x = 26    or      5x +16 = 26

  

 Dan has five times as many $1 bills as $5 bills.  He has a total of 48 bills.  How many of each does he have?
    (Have the kids realized by now that the briefcase is the total or difference on the right side of the equal sign?

                         5x + x = 48    x is the $5 bills.  They tried to throw you off by using non variables in the problem. 



In my next blog, "The Spy Story Conclusion," we will solve these problems.