Answer :
Final answer:
To find the number of quarters and nickels in the bag, we can set up a system of equations and solve for the variables. Using elimination, we can find that there are 38 quarters and 155 nickels in the bag.
Explanation:
To solve this problem, we can set up a system of equations. Let's define the number of quarters as q and the number of nickels as n. We have two equations:
- q + n = 193 (since we know that there are a total of 193 coins)
- 0.25q + 0.05n = 17.25 (since the total value of the quarters and nickels is $17.25)
We can solve this system of equations using either substitution or elimination. Let's use elimination to solve for q. Multiply the first equation by 0.05 to eliminate n:
0.05q + 0.05n = 9.65
Now subtract the second equation from this new equation:
0.05q + 0.05n - (0.25q + 0.05n) = 9.65 - 17.25
-0.20q = -7.60
Divide both sides of the equation by -0.20:
q = 38
Now substitute this value of q back into the first equation to solve for n:
38 + n = 193
n = 155
So, there are 38 quarters and 155 nickels in the bag.
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