Question 592268: 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?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 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'.
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