1. ## Thrifty Shopping

Hilda was checking soap prices at the market and discovered that <font color=blue>Ample</font color=blue> was 50% more expensive than <font color=blue>Cleany</font color=blue>, and contained 20% less weight than <font color=blue>Breezy</font color=blue>. However, <font color=blue>Breezy</font color=blue> was 50% heavier than <font color=blue>Cleany</font color=blue>, and cost 25% more than <font color=blue>Ample</font color=blue>.

Which would be the best buy?

2. ## Re: Thrifty Shopping

On my calculations it is a toss up between <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>A and B</font color=yellow></span hi>

I have prices in the ratios <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow> 1.5 : 1.875 : 1</font color=yellow></span hi>
I have weights in the ratios <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow> 1.6 : 2 : 1</font color=yellow></span hi>
Which gives weight / Price ratios of <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow> 1.066... : 1.066... : 1</font color=yellow></span hi>

I guess I must have made a mistake somewhere.

StuartR

3. ## Re: Thrifty Shopping

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>Denote prices by PA, PB and PC and weights by WA, WB and WC.

PA = 3/2 PC so PC = 2/3 PA
PB =5/4 PA

WA = 4/5 WB so WB = 5/4 WA
WB =3/2 WC so WC = 2/3 WB = 5/6 WA

We see that B is both 25% heavier and 25% more expensive than A, so (as Stuart found) they are equivalent. C, however, weighs 1/6 less but costs 1/3 less, so C is the best buy.</font color=yellow></span hi>

4. ## Re: Thrifty Shopping

Nailed it ! <img src=/S/cheers.gif border=0 alt=cheers width=30 height=16>

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