A company sells detergent in three different sized boxes: small (S), Gauss School of Mathematical Science 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

 Sep 12, 2020

I think you mean best deal to worst deal, but I'll infer!

Let's say the small size has 100 gallons of detergent (I know right?!), and costs 100 dollars.


Then medium costs 150 dollars and has 80 gallons of detergent.

It should, to be a fair deal, cost 150 dollars with 150 gallons.


Obviously medium is worse than small.



where < means worse.


Large has 200 gallons of detergent, and costs 195 dollars!


It should cost, to be a fair deal, 200 dollars!


It is 5 dollars cheaper!


Therefore, Large, Small, Medium from best to worst. Unless the detergent has short shelf life...

 Sep 12, 2020

Amounts of detergent:

s = small

l = large =  2s

m = medium  =  .8 l  = 1.6s


Assign the unit cost of

small                         = 1  per unit


m = 1.5s / 1.6s         = .9375 per unit

l  =   (1.3)(1.5s) / 2s  = .975  per unit

so the cost per unit (best to worst)        medium     large    small   

 Sep 13, 2020

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