Pigs

A buyer said, "I want to buy 100 pigs for 100 denarii. An adult pig costs ten denarii, a sow five denarii, and two little piglets are worth one denarius. " How many pigs, cows, and piglets could he buy for exactly 100 denarii?

Correct answer:

a =  1
b =  9
c =  90

Step-by-step explanation:

$$\begin{gathered} 100=10a+5b+c/2 \\ a+b+c=100 \\ 200=20a+10b+c \\ 200=20a+10b+(100-a-b) \\ 100=19a+9b \\ a=1 \end{gathered}$$

$b=9$

$$\begin{gathered} c=100-a-b=100-1-9=90 \\ \text{ Verifying Solution: } \\ {p}_1=10\cdot a+5\cdot b+c/2=10\cdot 1+5\cdot 9+90/2=100 \\ {p}_2=a+b+c=1+9+90=100 \end{gathered}$$

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