SOLUTION: a jar containing only nickels and dimes contains a total of 50 coins. the value of all the coins in the jar is $4.10. find the amount of nickels and dimes that are in the jar?

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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'.