Bob wants to buy cards with $20. Each card cost between $1.80 and $2.25. What is the maximum number of cards he can buy?
Assuming there are no sales taxes, the maximum number of cards is
floor(20/1.8)=11
That is if he does not buy the more expensive cards.
Note:floor(x) is the biggest integer not exceeding x. In the above example, 20/1.8=11.111..., and the biggest integer that does not exceed 11.111 is 11.
if he buys the most expensive then he can only buy 8
To determine the maximum number of cards Bob can buy, we need to find the card with the highest cost that he can afford with his budget of $20. Then, we divide $20 by the cost of that card.
First, let's find the highest cost card Bob can afford:
We can calculate the maximum cost card by taking the budget of $20 and dividing it by the lowest denomination of $1.80.
$20 ÷ $1.80 = 11.11 (rounded to two decimal places)
Bob can afford 11 cards priced at $1.80.
However, we also need to check if he can afford any cards priced higher than $1.80. Let's calculate the number of cards he can afford at the higher price of $2.25:
$20 ÷ $2.25 = 8.89 (rounded to two decimal places)
Bob can only afford 8 cards priced at $2.25.
Now, we can determine the maximum number of cards he can buy. It will be the smaller value between the two calculated quantities, which is 8:
Therefore, Bob can buy a maximum of 8 cards.