Question

Molly bought a lollipop for $\:35$ cents. How many different ways could she have paid for it using dimes, nickels, and pennies from her piggy - bank, using all three coin-types? Solution:

Answer 1

Hint: To solve such questions first know the conversion of one coin-type to the other. For dimes, nickels, and pennies the conversion is as given below: A penny is worth $\:1$ cent. A nickel is worth $5$ cents. A dime is worth $\:10$ cents. $1$ Penny = $1$ cent, $1$ Nickel = $5$ cents, $1$ Dime = $\:10$ cents

Complete step by step answer:
The lollipop Molly bought was $\:35$ cents. Make as many combinations as possible of the different coin types that add up for a total of $\;35$ cents. Since Molly has to use all the three – coin-types, make sure to include all the three coin-types in the solution.
Way $1$ : Molly uses $1$ dime, $1$ nickel, and $\;20$ pennies.
$1$ Dime and $1$ Nickel $= 10 + 5 = 15$ cents.
Therefore, $35 - 15 = 20$ pennies would be required to reach the amount of $\;35$ cents.
Way $2$ : Molly uses $1$ dime, $2$ nickels, and $\:15$ pennies.
$2$ Nickel and $1$ Dime $= 10 + 10 = 20$ cents.
Therefore, $35 - 20 = 15$ pennies would be required to reach the amount of $\:35$ cents.
Way $3$ : Molly uses $1$ dime, $3$ nickels, and $\:10$ pennies.
$3$ Nickel and $1$ Dime $= 15 + 10 = 25$ cents.
Therefore, $35 - 25 = 10$ pennies would be required to reach the amount of $\:35$ cents.
Way $4$ : Molly uses $2$ dime, $1$ nickels, and $\;10$ pennies.
$1$ Nickel and $2$ Dime $= 5 + 20 = 25$ cents.
Therefore, $35 - 25 = 10$ pennies would be required to reach the amount of $\:35$ cents.
Way $5$ : Molly uses $2$ dime, $2$ nickels, and $5$ pennies
$2$ Nickel and $2$ Dime $= 10 + 20 = 30$ cents.
Therefore, $35 - 30 = 5$ pennies would be required to reach the amount of $\:35$ cents.
Way $6$ : Molly uses $1$ dime, $4$ nickels, and $5$ pennies
$4$ Nickel and $1$ Dime $= 20 + 10 = 30$ cents.
Therefore, $35 - 30 = 5$ pennies would be required to reach the amount of $\:35$ cents.
Therefore, there are $6$ different ways Molly could have paid for the lollipop.

Note: The only thing to take care of while solving these questions is to keep the conversion of one coin type to another in mind. Always start by writing the conversion formulae separately and then begin with the solution. Also, take care of whether the question is asking to include all three types of coins every time or one type can be excluded in some solutions.