Final answer:
To find the number of quarters in the collection of 38 coins worth $6.95, we set up a system of equations and solve it to find that there are 21 quarters in the collection.
Step-by-step explanation:
The question is asking to find the number of quarters in a collection of 38 coins, which are all either quarters or dimes, worth a total of $6.95. To solve this kind of problem, we use a system of equations based on the values and quantities of these coins.
Let's denote the number of quarters as Q and the number of dimes as D. We have two key pieces of information:
- The total number of coins is 38, which gives us the equation Q + D = 38.
- The total value of the coins is $6.95. Since quarters are worth $0.25 and dimes are worth $0.10, we get the equation 0.25Q + 0.10D = 6.95.
Now we can solve this system of equations using substitution or elimination. If we solve for one variable in the first equation, say D = 38 - Q, we can substitute it into the second equation:
0.25Q + 0.10(38 - Q) = 6.95
Which simplifies to:
0.25Q + 3.8 - 0.10Q = 6.95
0.15Q = 3.15
Q = 21
So, there are 21 quarters in the collection.