Question

Mike can buy baseball cards at 3 for 25 cents. If he sells the cards at 2 for 25 cents, how many will he have to buy and sell to earn $1.00 in profit?

Answer 1

Mike buys baseball cards at a rate of 3 cards for 25 cents, or equivalently, 12 cards for one dollar:

12 cards = $1.00

He then sells the cards at a rate of 2 cards for 25 cents, or equivalently, 8 cards for one dollar:

8 cards = $1.00

To earn a profit of one dollar, Mike needs to sell the cards for two dollars (since his cost is one dollar):

$2.00 = 2 x $1.00

To make a profit of one dollar, he needs to earn one dollar more than his cost, or $2.00 in total revenue:

$2.00 - $1.00 = $1.00

For each sale of 8 cards, Mike earns $1.00 in revenue, so he needs to sell 2 sets of 8 cards to earn $2.00 in revenue and $1.00 in profit:

2 sets of 8 cards = 16 cards

Therefore, Mike needs to buy and sell 16 baseball cards to earn a profit of $1.00.

Answer 2

Mike buys baseball cards at a rate of 3 cards for 25 cents, which means he pays 25/3 cents per card. If he sells the cards at a rate of 2 cards for 25 cents, then he earns 25/2 cents per card.

To earn $1.00 in profit, Mike needs to earn 100 cents in profit. Let's call the number of cards he needs to buy and sell "x".

The profit per card is the selling price per card minus the buying price per card:
Profit per card = (25/2) - (25/3) = 25/6 cents

To earn a profit of 100 cents, Mike needs to sell x cards with a profit of 25/6 cents per card:
100 cents = (25/6) cents per card * x cards

Solving for x, we get:
x = (100 cents) / (25/6 cents per card) = 24 cards

Therefore, Mike needs to buy and sell 24 baseball cards to earn $1.00 in profit.