Trent wants to buy 2 packs of trading cards for 3 dollars each. The trading card packs that Trent normally buys tend to come in packs of 6, 10, 12, or 15 cards. After selecting 2 packs, Trent found that the first pack of cards cost 25 cents per card, and the second pack cost 30 cents per card. Trent uses this information to write the equations below in order to compare c, the number of cards in each pack.
Equation for the number of cards in the first pack: c1 = 6x or 10x or 12x or 15x (where x represents the number of packs)
Equation for the number of cards in the second pack: c2 = 6y or 10y or 12y or 15y (where y represents the number of packs)
Total cost equation: 2(3) = 6 dollars
Cost of first pack equation: c1(0.25)
Cost of second pack equation: c2(0.30)
Total cost equation: 0.25c1 + 0.30c2 = 6
To compare the number of cards in each pack, Trent can write the following equations:
Equation 1: (6c) + (10c) = 3
This equation represents the total cost of the two packs. The first pack contains 6 cards (6c) and the second pack contains 10 cards (10c). The sum of the costs of these two packs should be equal to 3 dollars.
Equation 2: 0.25(6c) + 0.30(10c) = 3
This equation represents the total cost of the two packs, considering the cost per card. The first pack costs 25 cents per card (0.25 * 6c) and the second pack costs 30 cents per card (0.30 * 10c). The sum of the costs of these two packs should be equal to 3 dollars.
By solving these equations, Trent can determine the value of 'c' which represents the number of cards in each pack.