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
Let’s use variables to solve the problem:
- Let ppp represent the number of pennies.
- The number of quarters is 2p2p2p (since there are twice as many quarters as pennies).
- The number of nickels is 3p3p3p (since there are three times as many nickels as pennies).
- The number of dimes is 6×number of nickels6 \times \text{number of nickels}6×number of nickels = 6×3p=18p6 \times 3p = 18p6×3p=18p (since there are six times as many dimes as nickels).
We need to find how many more dimes there are compared to quarters:Difference=Number of dimes−Number of quarters=18p−2p=16p\text{Difference} = \text{Number of dimes} – \text{Number of quarters} = 18p – 2p = 16pDifference=Number of dimes−Number of quarters=18p−2p=16p
To find how many times more dimes there are than quarters, divide the difference by the number of quarters:16p2p=8\frac{16p}{2p} = 82p16p=8
So, there are 8 times as many dimes as quarters.
However, none of the provided options exactly match this result, so there might be a mistake in the problem statement or options. But based on the calculations:
The closest answer would be:
None of the provided options are correct (should be 8 times as many).