You have $5.00 in quarters and dimes. You have a total of 41 coins. How many of the coins are quarters?

To find the number of quarters, set up a system of equations. Solve the system to find the value of q. The number of quarters is 6. ;

Answered by SloanGarrett45 | 2024-06-18

Solving the system of equations, we find there are 6 quarters and 35 dimes that amount to 41 coins in total with a total value of $5.00.
Solving for the Number of Quarters
To find how many quarters you have, we can set up a system of equations:

Let q be the number of quarters.
Let d be the number of dimes.

We have the following equations based on the problem:

The total number of coins: q + d = 41
The total value in dollars: 0.25q + 0.10d = 5.00

First, we'll express d in terms of q using the first equation:
d = 41 - q
Next, substitute this expression into the second equation:
0.25q + 0.10(41 - q) = 5.00
Simplify and solve for q:
0.25q + 4.10 - 0.10q = 5.00
0.15q + 4.10 = 5.00
0.15q = 0.90
q = 6
Thus, there are 6 quarters and, substituting back, 35 dimes.

Answered by EdwardRow | 2024-06-25

There are 6 quarters among the total of 41 coins made up of quarters and dimes. This was found by setting up a system of equations for the total number of coins and their value. Using algebra, we determined the number of quarters and dimes in this scenario.
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Answered by EdwardRow | 2024-10-15