# How Many Ways Can You Make 50 Cents With Coins?

By Marty Gitlin

Considering the possibilities with all the coins in our currency, there are a number of combinations that can be used to create 50 cents. Thinking of the possibilities can be educational.

Benefits

This is an excellent math exercise for young students. It teaches them adding skills and gives them an idea of how many combinations there are to arrive at a particular number.

Types

Think of all the possibilities using a 50-cent piece as well as quarters, dimes, nickels and pennies.

Considerations

Start with the 50-cent piece. That’s one right there. Two quarters? That’s two. Five dimes? That’s three. Ten nickels? That’s four. Fifty pennies? That’s five.

Potential

Create combinations off one quarter. One quarter, two dimes and a nickel puts the count at six. One quarter and 25 pennies is seven, One quarter, one nickel and 20 pennies is eight. One quarter, two nickels and 15 pennies is nine. One quarter, three nickels and 10 pennies is 10. One quarter, four nickels and five pennies is 11. One quarter and five nickels is 12. One quarter, one dime and 15 pennies is 13. One quarter, two dimes and five pennies is 14. You have now used up all your possibilities with quarters.

Four dimes and 10 pennies gives you 15 options. Four dimes and two nickels is 16. Four dimes, one nickel and five pennies is 17. Three dimes and 20 pennies makes 18. Three dimes, one nickel and 15 pennies is 19. Three dimes, two nickels and 10 pennies is 20. Three dimes, three nickels and five pennies is 21. three dimes and four nickels is 22. Two dimes and 30 pennies is 23. Two dimes, one nickel and 25 pennies is 24. Two dimes, two nickels and 20 pennies is 25. Two dimes, three nickels and 15 pennies is 25. Two dimes, four nickels and 10 pennies is 26. Two dimes, five nickels and five pennies is 27. Two dimes and six nickels is 28. So much for the dimes.

One nickel and 45 pennies is 29. Two nickels and 40 pennies is 30. Three nickels and 35 pennies is 31. Four nickels and 30 pennies is 32. Five nickels and 25 pennies is 33. Six nickels and 20 pennies is 34. Seven nickels and 15 pennies is 35. Eight nickels and 10 pennies is 36. Nine nickels and five pennies is 37.

And that is your answer! There are 37 combinations of coins that can be used to create 50 cents.

Time Frame

Try this with your kids and see how long it takes them to find all the combinations. Give them 15 minutes and a small reward if they can get it done. That will provide a little extra motivation.

Significance

The ability to complete such an exercise will give confidence to kids in a subject in which many of them struggle. It will also provide them with an enjoying and challenging experience.