Figera has two 10% coins, six 20% coins and three 50% coins. What is the least number of coins that she can use to make $2?

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Worked solution

5

1. Convert the target amount to cents and determine the strategy to minimize the number of coins.

Target amount = $2=200\char36{}2 = 200 cents.
To use the least number of coins, we must use as many of the largest denomination coins as possible.

2. Use the maximum possible number of 50-cent coins.

We have three 5050-cent coins.
Value = 3×50=1503 \times 50 = 150 cents.
Number of coins used = 33.
Remaining amount = 200−150=50200 - 150 = 50 cents.

3. Use the next largest denomination (20-cent coins) for the remaining amount.

We need to make 5050 cents using 2020-cent and 1010-cent coins.
Maximum number of 2020-cent coins we can use without exceeding 5050 cents is 22.
Value = 2×20=402 \times 20 = 40 cents.
Number of coins used = 22.
Remaining amount = 50−40=1050 - 40 = 10 cents.

4. Use the 10-cent coins for the final remaining amount and find the total number of coins.

We need 1010 cents, which requires one 1010-cent coin.
Number of coins used = 11.
Total number of coins = 3+2+1=63 + 2 + 1 = 6.

Answer

66 (option 1)

AI analysis — may contain mistakes.

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