Mario bought some sweets at the market, where 3 chocolates cost the same as 2 popsicles and 2 lollipops cost the same as 5 chocolates.

a) Mario decided to return to the market with money to buy exactly 3 lollipops but decided to buy popsicles instead. How many popsicles did he manage to buy?

b) If he had used the money for 3 chocolates, 2 popsicles, and 2 lollipops to buy the maximum number of sweets possible, how many would he have bought?
Solution

a) 15 chocolates cost the same as 10 popsicles and the same as 6 lollipops. Therefore, 10 popsicles are worth the same as 6 lollipops, and consequently, 5 popsicles the same as 3 lollipops. Thus, with the money for 3 lollipops, Mario can buy 5 popsicles.

b) From the previous item, we saw that the largest number of sweets Mario can buy with the same amount of money is chocolates. If 2 popsicles are equivalent to 3 chocolates and 2 lollipops are equivalent to 5 chocolates, then the maximum number of sweets is $3+3+5=11$ chocolates.