Victoria has pennies, dimes, and quarters. She has a total of $26.28. There are two times as many dimes as pennies. There are five times as many quarters as pennies. How many of each coin does she have? Can you please show work?
To solve this problem, we can break it down into equations based on the given information.
Let's assume the number of pennies Victoria has is "p."
From the information given, we can say that:
- The number of dimes she has is two times the number of pennies, so it is 2p.
- The number of quarters she has is five times the number of pennies, so it is 5p.
Now, let's determine the value of each coin:
- The value of pennies is 0.01 dollars each. So, the total value of pennies is 0.01p dollars.
- The value of dimes is 0.1 dollars each. So, the total value of dimes is 0.1 * 2p = 0.2p dollars.
- The value of quarters is 0.25 dollars each. So, the total value of quarters is 0.25 * 5p = 1.25p dollars.
Since we know that Victoria has a total of $26.28, we can set up the equation:
0.01p + 0.2p + 1.25p = 26.28
Simplifying this equation, we get:
1.46p = 26.28
Dividing both sides by 1.46, we find:
p = 18
Now that we have the number of pennies, we can calculate the number of dimes and quarters:
- Dimes: 2p = 2 * 18 = 36
- Quarters: 5p = 5 * 18 = 90
Therefore, Victoria has 18 pennies, 36 dimes, and 90 quarters.