Respuesta :
Answer:
Weight of silver coin = 29.25 units , weight of gold coin = 35.75 units
Explanation:
Let the weight of 1 gold coin be [tex]W_{1}[/tex]
Weight of 1 silver coin be [tex]W_{2}[/tex]
Total no of gold coins = 9
Total no of silver coins = 11
Total weight of gold coins = 9[tex]\times W_{1}[/tex]
Total weight of silver coins = 11[tex]\times W_{2}[/tex]
It is given that both weigh same thus we have
[tex]9W_{1}=11W_{2}............(i)[/tex]
After replacing coins the weights become as under
[tex]Gold Stack\\9W_{1}-W_{1}+W_{2}=8W_{1}+W_{2}\\\\SilverStack\\\\11W_{2}-W_{2}+W_{1}=10W_{2}+W_{1}[/tex]
Now it is given that gold stack weighs 13 unit less thus adding 13 units to gold stack gives it's weight equal to silver stack
the above relation modifies as
[tex]8W_{1}+W_{2}+13=10W_{2}+W_{1}\\7W_{1}+13=9W_{2}..........(ii)[/tex]
[tex]8W_{1}+W_{2}+13=10W_{2}+W_{1}\\7W_{1}+13=9W_{2}..........(ii)\\\\7\frac{11W_{2}}\\\\Solving equation i and ii we get\\\\{9}+13=9W_{2}\\\\77W_{2}+117=81W_{2}\\\\4W_{2}=117\\\\W_{2}=\frac{117}{4}=29.25units\\\\W_{1}=\frac{11W_{2}}{9}=35.75units[/tex]
