Question 83855
Let x=# of nickels, y= # of dimes

Since we know there is 50 coins, the sum of the coins is 50

{{{x+y=50}}}

And we also know that all of the coins are worth $3.50, so we have this equation

{{{0.05x+0.1y=3.5}}}


{{{100(0.05x+0.1y)=100(3.5)}}} Multiply both sides by 100 to make every number whole


{{{5x+10y=350}}}


So we now have the system of equations 


{{{x+y=50}}}
{{{5x+10y=350}}}


Now lets solve this system by addition


*[invoke solving_linear_system_by_elimination 1, 1, 50, 5, 10, 350]


So there are 30 nickels and 20 dimes



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Let x=beans that sell for $9, y=beans that sell for $12


{{{x+y=100}}} here is the sum of the 2 beans which equals the target weight
{{{9x+12y=11.25*100}}} "The two types are mixed to create 100lb of a mixture that will sell for $11.25 per pound"


So we have the system of equations


{{{x+y=100}}}
{{{9x+12y=1125}}}



Now lets solve this system by addition


*[invoke solving_linear_system_by_elimination 1, 1, 100, 9, 12, 1125] 


So we need 25 pounds of coffee beans that sell for $9 a pound and 75 pounds of coffee beans that sell for $12 a pound to make a 100lb mixture that will sell for $11.25 per pound.