Question

Damien was playing a card game with his sister. In order to come up with a strategy, he was trying to guess how many cards she was holding. He knew there are at most 50 cards in the deck and there were 10 cards in his hand and 12 cards in the discard pile. Write an inequality to represent how many cards Damien's sister could be holding. Explain how you know. Damien believes his sister has 28 cards. Explain why this is or is not possible.

Answer 1

Damien is correct, it is possible

Explanation:

This is possible, here is why. Damien has 10 cards in his hand. Do 10 - 50. You get 40. There are 12 cards in the pile. Do 12-40 and then you get 28. So yes, this is possible. Damien is correct!

Answer 2

`Sister \leq 28`

Explanation:

Given

`Total = 50` --- at most

`Damien = 10`

`Discard\ Pile = 12`

Required

Represents the card with his sister as an inequality.

At any given time, the relationship between number of cards is:

`Damien + Discard\ Pile + Sister \leq Total`

Where
`\leq` represents at most

Substitute values in
`Damien + Discard\ Pile + Sister \leq Total`

`10 + 12 + Sister \leq 50`

`22 + Sister \leq 50`

Collect Like Terms

`Sister \leq 50 - 22`

`Sister \leq 28`

The inequality shows that her sister could have at most 28 cards.

Because of this, Damien's belief is correct.