Sherry is playing the integer game and is given a chance to discard a set of matching cards. Sherry determines that if she discards one set of cards her score will increase by 12. If she discards another set, then her score will decrease by eight. If her matching cards make up all six cards in her hand, what cards are in Sherry's hand? Are there any other possibilities?
2,3,5,7,8,6
Let's assume that Sherry's score before discarding any cards is 'S'. If she discards a set and her score increases by 12, then her new score will be 'S + 12'. If she discards another set and her score decreases by eight, then her new score will be 'S + 12 - 8'.
Since her matching cards make up all six cards in her hand, we can say that Sherry initially had six matching cards. Let's represent these cards as 'x' for simplicity.
So, her initial score before any discards would be 6x.
If she discards a set and her score increases by 12, we can say that her new score is 6x + 12.
And if she discards another set and her score decreases by eight, her new score would be (6x + 12) - 8.
So, we have the equation: (6x + 12) - 8 = 6x.
Simplifying the equation, we get: 6x + 4 = 6x.
But this equation does not have a valid solution. It implies that 4 = 0, which is not true.
Therefore, there are no possible values for Sherry's cards in this scenario.
There are no other possibilities of cards in Sherry's hand that will meet the given conditions.
To find the cards in Sherry's hand, let's start by assigning variables to the number of matching cards she discards. Let's say she discards 'x' sets of matching cards.
According to the given information, if she discards one set of cards, her score will increase by 12. This means that 1 set of cards is equal to a score increase of 12 marks. So, we can write the equation for the score increase as:
1x = 12
Similarly, if she discards another set of cards, her score will decrease by 8. This means that 1 set of cards is equal to a score decrease of 8 marks. So, we can write the equation for the score decrease as:
1x = -8
Since her matching cards make up all six cards in her hand, the total number of sets is equal to the number of cards divided by the number of cards per set. In this case, it would be:
6 cards / 1 card per set = 6 sets
Now, we can substitute the value of 'x' in the equations to find the value of one set of cards:
1x = 12
x = 12
1x = -8
x = -8
The value of 'x' cannot be both 12 and -8 at the same time. Therefore, there seems to be no possible value of 'x' that satisfies both equations simultaneously. Hence, there are no possible values for the number of matching cards in Sherry's hand, and we cannot determine the specific cards in her hand based on the given information.