Question #190612

**Once upon a time Miss ABC invited 50 enemies to dinner. The piece de resistance was to be poison. In those crude days only two poisons were on the market, poison X and poison Y. **

a.**If she used more than one-half pound of poison, the guests would detect it and refuse to eat.**

b.**Miss ABC’s own private witch, a medieval version of the modern planning staff, once pronounced some magic numbers for her in the following doggerel:**

**One Y and X two,**

**If less than half,**

**Then woe to you.**

c.**Poison X will kill 75 and poison Y will kill 200 people per pound.**

d.**Poison X costs 100 solid gold pieces per pound, and poison Y 400 solid gold pieces per pound.**

**After devising a menu to cover up the taste of the poison, ABC found she was very short of solid gold pieces. In fact, unless she were very careful she would not be able to have another scheduled poisoning orgy that month. **

**Assist the alchemist in solving the problem, using graphical methods. The penalty for failure will be an invitation to next month’s dinner**

Expert's answer

Ok, Miss ABC can use 0.5 pounds of poison maximum. The price should be minimised, and the effect should be 50 people killing. Let the mass of X be x pounds, then mass of y is 0.5 - x pounds.

75x+200(0.5-x)=50

75x+100-200x=50

125x=50

x=0.4 (pound)

then y = 0.5-0.4=0.1 (pound)

The total price will be 0.4(100)+0.1(400)=80 (gold pieces)

**Answer: 0.4 pounds X, 0.1 pounds Y, 80 gold pieces.**

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