G
Guest
Guest
How many ways can you give change for one dollar, $1.
thank you in advance
thank you in advance
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This is a counting problem, not arithmetic.
What coins can you use?. If it's quarters, nickels, dimes, and pennies, then:
The number of ways to get a sum of 100 by adding 25,10,5,1 is the coefficient of \(\displaystyle x^{100}\) in the expansion of:
\(\displaystyle \L\\(1+x^{25}+x^{50}+....)(1+x^{10}+x^{20}+x^{30}+....)(1+x^{5}+x^{10}+x^{15}+....)(1+x+x^{2}+x^{3}+x^{4}+...)\\=\frac{1}{(1-x^{25})(1-x^{10})(1-x^{5})(1-x)}\)
You will find the coefficient of \(\displaystyle x^{100}\) is 242.
Using quarters, dimes, nickels and pennies there are 242 ways to make change for a dollar. It's 293 if you also use half-dollars.
What coins can you use?. If it's quarters, nickels, dimes, and pennies, then:
The number of ways to get a sum of 100 by adding 25,10,5,1 is the coefficient of \(\displaystyle x^{100}\) in the expansion of:
\(\displaystyle \L\\(1+x^{25}+x^{50}+....)(1+x^{10}+x^{20}+x^{30}+....)(1+x^{5}+x^{10}+x^{15}+....)(1+x+x^{2}+x^{3}+x^{4}+...)\\=\frac{1}{(1-x^{25})(1-x^{10})(1-x^{5})(1-x)}\)
You will find the coefficient of \(\displaystyle x^{100}\) is 242.
Using quarters, dimes, nickels and pennies there are 242 ways to make change for a dollar. It's 293 if you also use half-dollars.
G
Guest
Guest
thanking you Galactus
That is the correct answer! I needed a helping hand and you have given me that...
That is the correct answer! I needed a helping hand and you have given me that...
this is Counting
Hi, Well You can Do it many ways By using pennies, dimes, nickles, and quarters. There are Probebly More than This way But these are the main ones.
You Can do 100 pennies
4 quarters
10 dimes
20 Nickles Or
1. 0 quarters, 0 dimes, and 20 nickels. 2. 0 quarters, 1 dime, and 18 nickels. 3. 0 quarters, 2 dimes, and 16 nickels. 4. 0 quarters, 3 dimes, and 14 nickels. 5. 0 quarters, 4 dimes, and 12 nickels. 6. 0 quarters, 5 dimes, and 10 nickels. 7. 0 quarters, 6 dimes, and 8 nickels. 8. 0 quarters, 7 dimes, and 6 nickels. 9. 0 quarters, 8 dimes, and 4 nickels.10. 0 quarters, 9 dimes, and 2 nickels.11. 0 quarters, 10 dimes, and 0 nickels.12. 1 quarter, 0 dimes, and 15 nickels.13. 1 quarter, 1 dime, and 13 nickels.14. 1 quarter, 2 dimes, and 11 nickels.15. 1 quarter, 3 dimes, and 9 nickels.16. 1 quarter, 4 dimes, and 7 nickels.17. 1 quarter, 5 dimes, and 5 nickels.18. 1 quarter, 6 dimes, and 3 nickels.19. 1 quarter, 7 dimes, and 1 nickel.20. 2 quarters, 0 dimes, and 10 nickels.21. 2 quarters, 1 dime, and 8 nickels.22. 2 quarters, 2 dimes, and 6 nickels.23. 2 quarters, 3 dimes, and 4 nickels.24. 2 quarters, 4 dimes, and 2 nickels.25. 2 quarters, 5 dimes, and 0 nickels.26. 3 quarters, 0 dimes, and 5 nickels.27. 3 quarters, 1 dime, and 3 nickels.28. 3 quarters, 2 dimes, and 1 nickel.29. 4 quarters, 0 dimes, and 0 nickels.
Hi, Well You can Do it many ways By using pennies, dimes, nickles, and quarters. There are Probebly More than This way But these are the main ones.
You Can do 100 pennies
4 quarters
10 dimes
20 Nickles Or
1. 0 quarters, 0 dimes, and 20 nickels. 2. 0 quarters, 1 dime, and 18 nickels. 3. 0 quarters, 2 dimes, and 16 nickels. 4. 0 quarters, 3 dimes, and 14 nickels. 5. 0 quarters, 4 dimes, and 12 nickels. 6. 0 quarters, 5 dimes, and 10 nickels. 7. 0 quarters, 6 dimes, and 8 nickels. 8. 0 quarters, 7 dimes, and 6 nickels. 9. 0 quarters, 8 dimes, and 4 nickels.10. 0 quarters, 9 dimes, and 2 nickels.11. 0 quarters, 10 dimes, and 0 nickels.12. 1 quarter, 0 dimes, and 15 nickels.13. 1 quarter, 1 dime, and 13 nickels.14. 1 quarter, 2 dimes, and 11 nickels.15. 1 quarter, 3 dimes, and 9 nickels.16. 1 quarter, 4 dimes, and 7 nickels.17. 1 quarter, 5 dimes, and 5 nickels.18. 1 quarter, 6 dimes, and 3 nickels.19. 1 quarter, 7 dimes, and 1 nickel.20. 2 quarters, 0 dimes, and 10 nickels.21. 2 quarters, 1 dime, and 8 nickels.22. 2 quarters, 2 dimes, and 6 nickels.23. 2 quarters, 3 dimes, and 4 nickels.24. 2 quarters, 4 dimes, and 2 nickels.25. 2 quarters, 5 dimes, and 0 nickels.26. 3 quarters, 0 dimes, and 5 nickels.27. 3 quarters, 1 dime, and 3 nickels.28. 3 quarters, 2 dimes, and 1 nickel.29. 4 quarters, 0 dimes, and 0 nickels.