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:

  1. q + n = 193 (since we know that there are a total of 193 coins)
  2. 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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