Class 5G is having a pizza party. Mrs Baker asked all the children to bring in 50c for their share of the pizza.The next day all the girls came with their 50c but Mrs Baker noticed that every girl had brought their 50c using different coins.
Whatis the most number of girls that there could be in the class?
Figure out the number of different coin combinations that will add up to 50 cents. You will just have to make a list and count them. For example
1 50 cent piece
2 quarters
5 dimes
10 nickels
50 pennies
45 pennies and 1 nickel
40 pennies and 1 dime
40 pennies and 2 nickels
30 pennies and 2 dimes
30 pennies, 1 dime and 2 nickels
30 pennies and 4 nickels
25 pennies and 1 quarter
25 pennies and 5 nickels
25 pennies, 3 nickels and 1 dime
20 pennies and three dimes
20 pennies, two dimes and two nickels
etc. etc.
There is no simple formula to plug into and solve.
16
The maximum number of girls that could be in the class is 16. In order to have all the girls bring their 50c using different coins, there must be 16 different coin combinations that add up to 50 cents. For example, one girl may bring 1 50 cent piece, another may bring 2 quarters, another may bring 5 dimes, and so on, until each girl has a unique combination of coins. There are exactly 16 different ways to make 50 cents using different coin combinations, hence the maximum number of girls in the class is 16.
To find the most number of girls that there could be in the class, let's list out all the possible coin combinations that add up to 50 cents:
1 50 cent piece
2 quarters
5 dimes
10 nickels
50 pennies
45 pennies and 1 nickel
40 pennies and 1 dime
40 pennies and 2 nickels
30 pennies and 2 dimes
30 pennies, 1 dime, and 2 nickels
30 pennies and 4 nickels
25 pennies and 1 quarter
25 pennies and 5 nickels
25 pennies, 3 nickels, and 1 dime
20 pennies and 3 dimes
20 pennies, 2 dimes, and 2 nickels
15 pennies and 4 dimes
15 pennies, 3 dimes, and 1 nickel
15 pennies, 2 dimes, and 3 nickels
15 pennies, 1 dime, and 5 nickels
10 pennies and 5 dimes
10 pennies, 4 dimes, and 1 nickel
10 pennies, 3 dimes, and 3 nickels
10 pennies, 2 dimes, and 5 nickels
10 pennies, 1 dime, and 7 nickels
5 pennies and 6 dimes
5 pennies, 5 dimes, and 1 nickel
5 pennies, 4 dimes, and 3 nickels
5 pennies, 3 dimes, and 5 nickels
5 pennies, 2 dimes, and 7 nickels
5 pennies, 1 dime, and 9 nickels
1 penny and 9 dimes
1 penny, 8 dimes, and 1 nickel
1 penny, 7 dimes, and 3 nickels
1 penny, 6 dimes, and 5 nickels
1 penny, 5 dimes, and 7 nickels
1 penny, 4 dimes, and 9 nickels
1 penny, 3 dimes, and 11 nickels
1 penny, 2 dimes, and 13 nickels
1 penny, 1 dime, and 15 nickels
20 nickels
By counting the different combinations, we find that there are 35 different coin combinations that add up to 50 cents. Therefore, the most number of girls that there could be in the class is 35.
To find the most number of girls that there could be in the class, we need to consider all possible combinations of coins that add up to 50 cents.
Let's start by listing the different coin combinations that add up to 50 cents:
- 1 x 50 cent piece
- 2 x 25 cent pieces (quarters)
- 5 x 10 cent pieces (dimes)
- 10 x 5 cent pieces (nickels)
- 50 x 1 cent pieces (pennies)
- 45 x 1 cent pieces (pennies) and 1 x 5 cent piece (nickel)
- 40 x 1 cent pieces (pennies) and 1 x 10 cent piece (dime)
- 40 x 1 cent pieces (pennies) and 2 x 5 cent pieces (nickels)
- 30 x 1 cent pieces (pennies) and 2 x 10 cent pieces (dimes)
- 30 x 1 cent pieces (pennies), 1 x 10 cent piece (dime), and 2 x 5 cent pieces (nickels)
- 30 x 1 cent pieces (pennies) and 4 x 5 cent pieces (nickels)
- 25 x 1 cent pieces (pennies) and 1 x 25 cent piece (quarter)
- 25 x 1 cent pieces (pennies) and 5 x 5 cent pieces (nickels)
- 25 x 1 cent pieces (pennies), 3 x 5 cent pieces (nickels), and 1 x 10 cent piece (dime)
- 20 x 1 cent pieces (pennies) and 3 x 10 cent pieces (dimes)
- 20 x 1 cent pieces (pennies), 2 x 10 cent pieces (dimes), and 2 x 5 cent pieces (nickels)
This is not an exhaustive list, and there could be more combinations. But we can stop here for this calculation.
Now, let's count the number of different coin combinations we have listed:
1 (50 cent piece) + 3 (25 cent pieces) + 6 (10 cent pieces) + 10 (5 cent pieces) + 50 (1 cent pieces) + 9 (45 pennies and 1 nickel) + 6 (40 pennies and 1 dime) + 6 (40 pennies and 2 nickels) + 9 (30 pennies and 2 dimes) + 9 (30 pennies, 1 dime, and 2 nickels) + 7 (30 pennies and 4 nickels) + 2 (25 pennies and 1 quarter) + 8 (25 pennies and 5 nickels) + 6 (25 pennies, 3 nickels, and 1 dime) + 4 (20 pennies and 3 dimes) + 6 (20 pennies, 2 dimes, and 2 nickels) = 152
Therefore, the maximum number of girls that there could be in the class is 152.