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In this question, form two equations to represent the total number of coins and the total values of the coins. Then after forming the equations, solve them simultaneously.

We know that a dime = $0.10 and a nickel = $0.05

Let x represent the number of dimes and y represent nickels,

therefore:

a) x + y = 61

b)0.1x + 0.05y = 4.15

The second equation can be rewritten by multiplying the decimals by 100 to get

10x + 5y = 415

so 2x + y = 83

Solve the two equations simultaneously i.e.

a) x+y=61

b)2x+y=83

Therefore x=22 and y=39

Hence there are 22 dimes in the jar

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