A child has a bottle full of pennies, nickels, dimes, and quarters. There are twice as many quarters as pennies, four times as many as nickels as pennies, and five times as many dimes as nickels. How many more dimes does the child have than quarters?
A.
4 times as many
B.
5 times as many
C.
20 times as many
D.
10 times as many
Let’s define the variables to solve the problem:
- Let ppp represent the number of pennies.
- The number of quarters is 2p2p2p (twice as many as pennies).
- The number of nickels is 4p4p4p (four times as many as pennies).
- The number of dimes is 5×4p=20p5 \times 4p = 20p5×4p=20p (five times as many as nickels).
To find how many more dimes the child has than quarters:
- Calculate the number of dimes:Number of dimes=20p\text{Number of dimes} = 20pNumber of dimes=20p
- Calculate the number of quarters:Number of quarters=2p\text{Number of quarters} = 2pNumber of quarters=2p
- Find the difference between the number of dimes and quarters:Difference=20p−2p=18p\text{Difference} = 20p – 2p = 18pDifference=20p−2p=18p
- Determine how many times the number of dimes is compared to the number of quarters:Ratio=20p2p=10\text{Ratio} = \frac{20p}{2p} = 10Ratio=2p20p=10
So, the child has 10 times as many dimes as quarters.
The correct answer is:
D. 10 times as many