Question 592268
Let d = number of dimes and q = number of quarters


Since "a jar containing only nickels and dimes contains a total of 50 coins", we know that 


d+q = 50


Basically take the individual totals of each and add them up to get 50 coins total.


This is equation 1.



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If you have d dimes, then the total value of them is 0.1d dollars.


If you have q quarters, then the total value is 0.25q dollars


These two add to:   0.1d + 0.25q


and this expression is equal to $4.10, so...


0.1d + 0.25q = 4.10


Now multiply everything by 100 to get


10d + 25q = 410


This is equation 2.

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So we have two equations


d+q = 50 
10d + 25q = 410



with 2 unknowns. So you can either use substitution or elimination to solve.



I recommend substitution. Solve for d  to get d = 50 - q, then substitute this into 10d+25q = 410 to get


10(50-q) + 25q = 410


From here, you can solve for q, which I'll let you do.



Once you have the value of 'q', use it to find the value of 'd'.