Coin count

Eve had seven coins. Crowns, two-crowns, and five-crowns. At least two of each. How many did she have if she could buy three packs of gum for six crowns?

Final Answer:

a =  2
b =  3
c =  2

Step-by-step explanation:

$$\begin{gathered} x=3\cdot 6=18 \\ a+b+c=7 \\ x=1\cdot a+2\cdot b+5\cdot c \\ a>1,b>1,c>1 \\ c=2 \\ a+2b=x-2\cdot 5 \\ a+b=5 \\ a=2 \\ b=5-a=5-2=3 \\ {k}_1=1\cdot a+2\cdot b+5\cdot c=1\cdot 2+2\cdot 3+5\cdot 2=18 \\ {k}_2=a+b+c=2+3+2=7 \end{gathered}$$

$b=3$

$c=2$

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