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?
+237 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
