A child has a bottle full of pennies, nickels, dimes, and quarters. There are twice as many quarters as pennies, three times as many as nickels as pennies, and six times as many dimes as nickels. How many more dimes does the child have than quarters?
A.
10 times as many
B.
5 times as many
C.
6 times as many
D.
9 times as many
The Correct answer and Explanation is:
To solve the problem, let’s define the number of pennies as ppp.
- Quarters: There are twice as many quarters as pennies, so the number of quarters is 2p2p2p.
- Nickels: There are three times as many nickels as pennies, so the number of nickels is 3p3p3p.
- Dimes: There are six times as many dimes as nickels, so the number of dimes is 6×3p=18p6 \times 3p = 18p6×3p=18p.
Now, we need to determine how many more dimes the child has than quarters:
- Difference between dimes and quarters: 18p−2p=16p18p – 2p = 16p18p−2p=16p
To find how many times more dimes there are than quarters, we divide the difference by the number of quarters:Number of times more dimes than quarters=16p2p=8\text{Number of times more dimes than quarters} = \frac{16p}{2p} = 8Number of times more dimes than quarters=2p16p=8
Since the answer choices do not include 8 times as many, it appears there was a mistake in the interpretation of the problem. Let’s reassess:
The question asks for the ratio between the number of dimes and quarters, which is:18p2p=9\frac{18p}{2p} = 92p18p=9
Thus, the child has 9 times as many dimes as quarters.
Final Answer:
The correct answer is D. 9 times as many.