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A breakfast cereal is sold in 3 sized boxes, micro, standard and large. A store has 444 boxes of cereal in total. The ratio of the number of micro boxes to standard boxes is 3:1. In one day the store  sells 60% of the micro boxes, 25% of the large boxes and none of the standard boxes. There are now 285 boxes left in total. How many of each size box was there at the start?

 Apr 23, 2022
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Let number of micro boxes be m

                       standard boxes be s

                       large boxes be l

           m : s = 3 : 1

                    = 3x and x

     m + s + l = 444

   or, 3x + x + l = 444

    or, 4x + l = 444 .... (1)

     60% micro and 25% large boxes are sold.

          40/100m + s + 75/100l = 285

        or, 40/100 * 3x + x + 75l/100 = 285

        or, (200x + 75l)/100 = 285

        or, 220x + 75l = 285 * 100

        or, 44x + 15l = 5700 .... (2)

Multiplying, eqn. (1) by 15 and subtracting eqn (2) from

              eqn (1) we get 

                60x + 15 l = 6660

                44x + 15 l = 5700

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

               16x        =    960

                   x = 60

Putting value of x in eqn (1) -> 240 + l = 444

                                                or, l = 204

      Micro boxes = 30 * 6 = 180

      Standard boxes = 60

      Large boxes = 204

 Apr 24, 2022

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