SOLUTION: Amber makes toys for the children in the Children’s Hospital at Christmas. She makes wagons (with four wheels) and trikes (with 3 wheels). She used 68 wheels for the toys for l

Algebra ->  Equations -> SOLUTION: Amber makes toys for the children in the Children’s Hospital at Christmas. She makes wagons (with four wheels) and trikes (with 3 wheels). She used 68 wheels for the toys for l      Log On


   

Question 1180507: Amber makes toys for the children in the Children’s Hospital at Christmas.
She makes wagons (with four wheels) and trikes (with 3 wheels). She used 68
wheels for the toys for last Christmas. What number of wagons and trikes might
she have made? Make sure you can verify you have all possibilities.
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Wagons, 4 wheels each
Tricycles, 3 wheels each
68 wheels used

if t Trikes and w Wagons then 4w%2B3t=68. Look for any combinations of nonzero, non-negative whole numbers w and t.


t=%2868-4w%29%2F3%29------find any or as many whole number combinations you want.

5 wagons 16 trikes.

If you test some lower values for w, you could find:
Wagons    Trikes
  2         20
  5         16
  8         12
 11          8
 14          4

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Amber makes toys for the children in the Children’s Hospital at Christmas.
She makes wagons (with four wheels) and trikes (with 3 wheels). She used 68
wheels for the toys for last Christmas. What numbers of wagons and trikes
might she have made? Make sure you can verify you have all possibilities.
Let t be the number of trikes and w be the number of wagons. So:

3t + 4w = 68

Solve for w

     4w = 68 - 3t
    
      w = 17 - (3t)/4

(3t)/4 must be a whole number so t must be a multiple of 4, to make 
(3t)/4 a whole number. [0 is a multiple of 4 so we must include 0.]

      t       17-(3t)/4     =      w
    -------------------------------- 
      0       17-   0/4 = 17- 0 = 17
      4       17-  12/4 = 17- 3 = 14
      8       17-  24/4 = 17- 6 = 11
     12       17-  36/4 = 17- 9 =  8
     16       17-  48/4 = 17-12 =  5
     20       17-  60/4 = 17-15 =  2

There are 6 possibilities.

[The other tutor left out the possibility that Amber could have made 17
wagons and no trikes, but there is no reason she couldn't have made only
wagons.  We just know that she used all 68 wheels with none left over.]

Edwin