10.A deck of cards was dealt out equally to 7 people with 2 remaining cards. How many cards were in the deck originally? Let $c$ represent the total number of cards.

Step 1 ：Given that the deck of cards was dealt out equally to 7 people with 2 remaining cards, we can set up the following equation: \(7p + 2 = c\), where p is the number of cards each person received and c is the total number of cards in the deck.

Step 2 ：The number of cards each person received must be a whole number, because you can't deal out a fraction of a card. Therefore, the total number of cards, c, must be a multiple of 7 plus 2.

Step 3 ：The smallest multiple of 7 is 7 itself, but \(7 + 2 = 9\), which is less than the minimum number of cards in a deck (which is 52 in a standard deck). So we need to find a multiple of 7 that, when 2 is added, gives a number greater than or equal to 52.

Step 4 ：The next multiple of 7 is 14, but \(14 + 2 = 16\), which is still less than 52. We continue this process until we find a suitable multiple.

Step 5 ：The multiple of 7 that gives a number greater than or equal to 52 when 2 is added is \(7 * 7 = 49\). When we add 2 to 49, we get 51, which is still less than 52.

Step 6 ：The next multiple of 7 is \(7 * 8 = 56\). When we add 2 to 56, we get 58, which is greater than 52.

Step 7 ：Therefore, the total number of cards in the deck was \(\boxed{58}\).