Peter spent 1 3 of his money on a toy car and 2 3 of the remainder on a toy boat. He had $6 left. How much money did he spend altogether?

Question

how to solve step by step

Answer 1

First we need to find the amt.he had to begin with, so let that be represented by x

 

1/3 of x spent leaves 2/3 of x as the remainder.

 

But he only spent 2/3 of the remainder or 2/3 of (2/3 of x) or 4/9 x

starting amt. -  money for car - amt.for boat  = 6

 

       x           -     1/3 x           - (2/3)(2x/3)   = 6

 

Solving by multiplying both sides by 9:

 

      9x           -       3 x            -  4x               = 54

 

                                                2x                = 54

                                          

                                                  x                = 27

 

Amt.spent altogether is 27 - 6 = 21.

 

Solve using common denominator:

 

x      -   1/3 x    -    (2/3)(2x/3)   =  6

 

3x/3 -    x/3      -        4x/9         =  6

 

Getting a common denominator:

 

9x             3x                  4x                    54

------   -   ------      -       -----           =    ------

 9               9                    9                     9

 

 

2x                                                   =     54

 

 

 

2x        54

---  =   ----

2           2

 

 

x = 27, same, same.