Final answer:
The correct statements concerning the ratios are that the ratio of quarters to pennies is 7:9 and the ratio of quarters to total coins is 7:24. The other provided statements regarding the ratios are incorrect.
Step-by-step explanation:
The task involves understanding ratios and proportions between different coins. Here, we examine several statements to identify which of them are correct based on the given quantities of each type of coin.
- The ratio of dimes to pennies is given as 9:5. Since there are 27 pennies and 15 dimes, the simplified ratio would be 15/27, which reduces to 5/9, thus the statement is incorrect.
- The ratio of nickels to quarters is purported to be 3:9. There are 9 nickels and 21 quarters, which simplifies to a ratio of 3:7, not 3:9, making this statement incorrect as well.
- For the ratio of quarters to pennies, stated as 7:9, we have 21 quarters and 27 pennies. This simplifies to a ratio of 7:9, so this statement is correct.
- The ratio of pennies and nickels to quarters is said to be 21:36. Adding the pennies and nickels gives us 36 (27 pennies + 9 nickels), and there are 21 quarters. The ratio should be 36:21, which simplifies to 12:7, so this statement is incorrect.
- Lastly, the ratio of quarters to total coins is described as 7:24. The total number of coins is 27 + 9 + 15 + 21 = 72. The ratio of quarters to the total number of coins is 21/72, which simplifies to 7:24. Hence this statement is correct.
The only correct statements are that the ratio of quarters to pennies is 7:9 and the ratio of quarters to total coins is 7:24.