a jar filled with only nickles and dimes contain a total of 61 coins. the value of all of the coins in the jar is $4.15. how many dimes are in the jar

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this is a typical 2 variable linear equation system, if we assume that the number of nickles and dime are x and y respectively, then we have

x+y = 61

and

5x+10y = 415

multiply first eq by 5

we have 5x+5y = 305

subtract it from the second equation, we have

5y = 415-305 = 110

y = 22

x = 39

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