A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 16% are pennies and 40% are dimes. There are 5 more nickels than pennies. How much money does the bag contain?
The Correct Answer and Explanation is:
To find how much money is in the bag, we start by identifying how many of each coin type there are.
Step 1: Total number of coins
There are 50 coins in the bag.
Step 2: Find the number of pennies
16% of the coins are pennies:
0.16×50=80.16 \times 50 = 80.16×50=8 pennies
Step 3: Find the number of dimes
40% of the coins are dimes:
0.40×50=200.40 \times 50 = 200.40×50=20 dimes
Step 4: Find the number of nickels
There are 5 more nickels than pennies:
Nickels = 8+5=138 + 5 = 138+5=13
Step 5: Find the number of quarters
Now that we know how many pennies, nickels, and dimes there are, we can find the number of quarters:
Pennies + Nickels + Dimes = 8 + 13 + 20 = 41
Total coins = 50
Quarters = 50−41=950 – 41 = 950−41=9
Step 6: Calculate the total value
- Pennies: 8×$0.01=$0.088 \times \$0.01 = \$0.088×$0.01=$0.08
- Nickels: 13×$0.05=$0.6513 \times \$0.05 = \$0.6513×$0.05=$0.65
- Dimes: 20×$0.10=$2.0020 \times \$0.10 = \$2.0020×$0.10=$2.00
- Quarters: 9×$0.25=$2.259 \times \$0.25 = \$2.259×$0.25=$2.25
Step 7: Add the values
Total money = $0.08 + $0.65 + $2.00 + $2.25 = $4.98
Explanation
This problem is solved by combining basic percentage calculation and simple arithmetic. The key is to interpret the percentages and relationships correctly. We start by using the total number of coins in the bag, which is given as 50. We know that 16 percent of the coins are pennies. This means multiplying 50 by 0.16 gives us the number of pennies, which is 8. Similarly, since 40 percent of the coins are dimes, multiplying 50 by 0.40 tells us there are 20 dimes.
The problem also states that there are five more nickels than there are pennies. Since we have already calculated that there are 8 pennies, this leads us directly to 13 nickels. At this point, we have accounted for 8 pennies, 20 dimes, and 13 nickels. Adding these gives a total of 41 coins. Since the total is supposed to be 50 coins, the remainder must be quarters. Subtracting 41 from 50 gives us 9 quarters.
Once we know how many of each coin we have, we multiply the quantity of each by its respective value. Pennies are worth one cent each, so 8 of them are worth 8 cents. Nickels are worth five cents each, dimes ten cents, and quarters twenty-five cents. After calculating the value for each group of coins, we add up all the values to find the total amount of money in the bag. The sum comes out to 4 dollars and 98 cents. This solution involves a straightforward application of percentages, basic addition, and multiplication.
