It’s a story– not a problem. Don’t create some problem you ain’t got. You can use algebra or not. Look.
Jack and Diane are playing poker. After one hand, Diane has 2 more chips than Jack. After the next hand, Diane wins 5 more chips from Jack. At this point, how many more chips does Diane have than Jack?
Explanation Using Algebra
Notice the word more in the question. We will never know how many chips each person has. The question asks what is the difference between Jack’s amount and Diane’s amount. So, the equation is (Diane) – (Jack) = (difference).
Now make some mathematical terms.
After the first hand, Diane has d chips. Jack has (d – 2). But then they play another hand, and Diane wins 5, which makes her term (d + 5). Jack loses 5 more, so Jack’s term is now (d – 7).
Subtract these two terms to find the difference.
(d + 5) – (d – 7) =
When the negative 1 in front of the second set of parentheses is distributed, the 7 becomes positive. The ds cancel, and the answer is 12.
Diane has 12 more chips than Jack.
Play god. Pretend you are some Greek god of fortune. Give Jack and Diane the same number of chips.
Jack = 10 , Diane = 10
After one hand, Diane has 2 more chips.
Jack = 9 , Diane = 11
After another hand, Diane wins 5 more.
Jack = 4, Diane =16
Now Diane has 12 more chips than Jack.