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A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs 50% more than the small size and contains 20% less detergent than the large size. The large size contains twice as much detergent as the small size and costs 30% more than the medium size. Rank the three sizes from best to worst buy .

A: SML

B: LMS

C: MSL

D: LSM

E: MLS

Select the most appropriate letter.

Aug 7, 2019

#1
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Let the small size cost  = C   and let the  volume of the  small  size be V

So....the unit cost for the  small size is  just  cost / volume  =   C/ V

The medium size  costs 50% more than the  small  size....so it  cost is  1.5C

The large size holds twice as  much as the  small size =  2V   and  costs 30% more than the medium size = (1.5)C (1.3)  = 1.95C

So...the unit  cost  for the large  size =  1.95C / 2V =   =   (195/200)C/V  =  (39/40)C/V =  .975C/V

Finally....the  medium size contains 20% less detergent than the large  size=   2V (.80)   = 1.6V

So....the uint  cost  for the  meduim  size  is  just   ( 1.5)C / (1.6 V) = (15/16)C/V  = .9375C/V

So.....best to worse we have

.9375C/V       .975C/V           C / V

M                   L                    S          ⇒        "E"   Aug 7, 2019
edited by CPhill  Aug 7, 2019