Crown

Siblings collect 2-crowns and 5-crowns. Together, have 80 coins with a total value of 310 crowns. How many saved two crowns, and how many five crowns?

Final Answer:

a =  30
b =  50

Step-by-step explanation:

$$\begin{gathered} a+b=80 \\ 2a+5b=310 \\ 2\cdot a+5\cdot b=310 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ -1.5b=-75 \\ b=\frac{-75}{-1.5}=50 \\ a=\frac{310-5b}{2}=\frac{310-5\cdot 50}{2}=30 \\ a=30 \\ b=50 \end{gathered}$$

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