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In Exercise 28, the clerk runs out of 10 cent coins and only has 3 and 8 cent coins left. It needs to be shown that the clerk can provide change for any amount of 14 cents or more.
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To prove that the clerk can make change for any value of 14 cents or higher, we can use a step-by-step approach.
Step 1: We start with the base case of 14 cents. By using one 8 cent coin and two 3 cent coins, we can make 14 cents.
Step 2: Now, let’s consider any value higher than 14 cents. We can use the same strategy as the base case. We start with one 8 cent coin and two 3 cent coins to make 14 cents.
Step 3: To make up the remaining value, we can add additional 3 cent coins. Since we have an unlimited supply of 3 cent coins, we can always make up the remaining value.
Step 4: Therefore, the clerk can make change for any value of 14 cents or higher.
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