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 .
Select the most appropriate letter.
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"