QuestionHow many ways can you use nickels, dimes, and quarters to pay for a 65-cent item? Answer: 18 ways.
Studdy Solution
STEP 1
Assumptions1. The vending machine accepts only nickels (5 cents), dimes (10 cents), and quarters (25 cents).
. The item costs65 cents.
3. We need to find the number of different ways to pay for the item.
STEP 2
We need to find the number of ways to combine nickels, dimes, and quarters to make up65 cents. We can do this by using a systematic approach and considering all possible combinations.
STEP 3
First, consider the case where we only use nickels. Since each nickel is worth5 cents, we would need13 nickels to make up65 cents. This is one possible way to pay for the item.
STEP 4
Next, consider the case where we use only dimes. Since each dime is worth10 cents, we would need6 dimes and1 nickel to make up65 cents. This is another possible way to pay for the item.
STEP 5
Next, consider the case where we use only quarters. Since each quarter is worth25 cents, we would need2 quarters and3 dimes to make up65 cents. This is another possible way to pay for the item.
STEP 6
Now, consider the case where we use a combination of nickels and dimes. We can create a table to systematically list all possible combinations.
STEP 7
Similarly, consider the case where we use a combination of nickels and quarters. We can add these combinations to our table.
STEP 8
Finally, consider the case where we use a combination of dimes and quarters. We can add these combinations to our table as well.
STEP 9
By considering all possible combinations of nickels, dimes, and quarters, we can count the total number of ways to pay for the65-cent item.
The total number of ways to pay for the65-cent item is18.
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