john has 24$ more than twice as much as brandon. together they have 150$. how much money each boy have

Question

system of equation

Answer 1

There are two equations in this system: (1) the sum of the money and (2) a relationship between how much money each boy possesses.  When possible, assign variables to the values the problem asks you to find (so you won't forget to convert values at the end of answering the problem).  For this problem, let:

  x = amount of money John has

  y = amount of money Brandon has

 

Translate:

  "john has 24$ more than twice as much as Brandon"       means

      x    =    24        +         2     *                y

 

  "together they have 150$"      means

      x   +   y       =     150

 

  "how much money each boy have"   means to report x and y

 

Now, the easy math:

     x = 24 + 2y             [re-write eq1]

     x + y = 150             [re-write eq2]

 

     (24+2y) + y = 150     [substitute value of x from eq1 into eq2]

      24 + 3y = 150           [combine like values]

        3y = 126                [subtract 24 from both sides]

           y = $42               [divide both sides by 3]

 

     x = 24 + 2(42)      [put y=42 into either equation to solve for x]

          x = $108

 

Checking (very important):

  Is $108 equal to $24 more than 2*($42)  ?

        108 = 24 + 84   ?

           108 = 108  ?yes

  Is  $108 + $42 = $150  ?

         150 = 150   ?yes

Answer 2

150 - 24 = x

 

x / 3 = y

 

y * 2 = z

 

z +24 = John's money

 

$150 - John's money = Brandon's money