Help - Word Problem

Question

The Sweater Shop sells sweaters in three colors: red $20, blue $25, white  $28. On Tuesday, they sold 23 sweaters. They sold seven more red sweaters than blue sweaters. They sold $522 in sweaters, how many Hite sweaters did they sell?

Answer 1

Let the number of sweaters sold be R, B, and W.

 

  "They sold $522 in sweaters"    means    R + B + W = 23      [eq1]

 

The dollars for all of each type of sweater is: 

      (dollars per sweater)*(number of sweaters).  So,

  "They sold $522 in sweaters"    means

     $20R + $25B + $28W = $522             [eq2]

 

  "They sold seven more red sweaters than blue sweaters" 

                 means  R = 7 + B             [eq3]

 

To do the math, let's use elimination.

 First, eliminate W:

    28R + 28B + 28W = 644        [28*eq1]

    20R + 25B + 28W = 522        [eq2]

---------------------------------     [elimination; subtract equations]

      8R +  3B            = 122

      3R  -  3B            =   21          [from eq3]

-------------------------------      [elimination, add equations]

      11R                   = 143

          R                  = 13          [divide both sides by 11]

          R  - B            =  7             [from eq3]

      ---------------------------    [elimination; subtract equations]

                B            =  6

 

       R + B + W = 23      [eq1]

      13 + 6 + W = 23             [insert values for R and B]

          19 + W = 23

              W = 4                  [subtract 19 from both sides]

 

Check:

  Is   13 + 6 + 4 = 23   ?

         23 = 23   ?yes

  Is   $20(13) + $25(6) + $28(4) = $522 

         260 + 150 + 112 = $522

         $522 = $522   ?yes

  Is  13 = 7 + 6   ?

       13 = 13   ?yes

    

Answer 2

Hi Mai Kou, to solve this, set up a system of equations. Let R represent the red sweaters, B represent the blue sweaters, and W represent the white sweaters.

 

Given:

 

Red = Blue + 7

 

Total sweaters sold = 23

 

Value of sweaters sold = $522

 

Equation 1:

 

R + B + W = 23

 

Equation 2:

 

20R + 25B + 28W = 522

 

Substitute R = B + 7 in both equations and simplify:

 

(B + 7) + B + W = 23

 

2B + W = 16

 

20 * (B + 7) + 25B + 28W = 522

 

45B + 28W = 382

 

Solve:

 

    2B   +    W  =   23

   45B  + 28W  = 382

  -----------------------

 

Multiply the first equation by -28 to eliminate the W terms:

 

 -56B   -  28W  = -448

  45B   + 28W  =   382

-------------------------

 

-11B = -66

 

Divide both sides by -11:

 

B = 6

 

6 blue sweaters were sold.

 

B + 7, or 13 red sweaters were sold.

 

Substituting into equation 1:

 

13 + 6 + W = 23

 

19 + W = 23

 

Subtract 19 from both sides:

 

W = 4

 

4 white sweaters were sold.

 

Questions?