At the end of a hockey season, a defenseman summarized his plus-minus total in a chart. For example, the first column shows that in five games during the season, his plus-minus total was +4. His plus-minus total for those 5 games was +20.
| No. of games | 5 | 13 | 8 | 6 | 12 | 2 | 17 | 9 |
| :------------ | :- | :- | :- | :- | :- | :- | :- | :- |
| plus-minus total | +4 | +3 | +2 | +1 | 0 | -1 | -2 | -3 |
Write an expression that will determine the defenseman's plus-minus total for all the games played during the season. What is his plus-minus total for the entire season?
Write an expression that will determine the plus-minus total for the season. Choose the correct answer below.
A. $(+4)-(+3)-(+2)-(+1)-(0)-(-1)-(-2)-(-3)$
B. $5(+4)-13(+3)-8(+2)-6(+1)-12(0)-2(-1)-17(-2)-9(-3)$
C. $(+4)+(+3)+(+2)+(+1)+(0)+(-1)+(-2)+(-3)$
D. $5(+4)+13(+3)+8(+2)+6(+1)+12(0)+2(-1)+17(-2)+9(-3)$
The defenseman's season plus-minus total is $\square$.
Answer (1)
The problem requires calculating a weighted sum based on the given table.
The correct expression is 5 ( + 4 ) + 13 ( + 3 ) + 8 ( + 2 ) + 6 ( + 1 ) + 12 ( 0 ) + 2 ( − 1 ) + 17 ( − 2 ) + 9 ( − 3 ) .
Calculate each term: 20 + 39 + 16 + 6 + 0 − 2 − 34 − 27 .
The defenseman's season plus-minus total is 18 .
Explanation
Understanding the Problem The problem provides a table summarizing a hockey defenseman's plus-minus statistics for the season. We need to determine the expression that calculates the total plus-minus and then compute the total. The table gives the number of games and the corresponding plus-minus total for those games. To find the overall plus-minus, we multiply the number of games by the plus-minus total for each category and then sum these products.
Formulating the Expression The expression to calculate the total plus-minus is:
5 ( + 4 ) + 13 ( + 3 ) + 8 ( + 2 ) + 6 ( + 1 ) + 12 ( 0 ) + 2 ( − 1 ) + 17 ( − 2 ) + 9 ( − 3 )
Calculating the Total Plus-Minus Now, let's calculate the total plus-minus:
5 × 4 = 20
13 × 3 = 39
8 × 2 = 16
6 × 1 = 6
12 × 0 = 0
2 × ( − 1 ) = − 2
17 × ( − 2 ) = − 34
9 × ( − 3 ) = − 27
Adding these values together:
20 + 39 + 16 + 6 + 0 + ( − 2 ) + ( − 34 ) + ( − 27 ) = 20 + 39 + 16 + 6 − 2 − 34 − 27 = 18
Final Answer The correct expression from the given options is:
D. 5 ( + 4 ) + 13 ( + 3 ) + 8 ( + 2 ) + 6 ( + 1 ) + 12 ( 0 ) + 2 ( − 1 ) + 17 ( − 2 ) + 9 ( − 3 )
The defenseman's season plus-minus total is 18.
Examples
Imagine you're managing a store and tracking daily profits and losses. The plus-minus system is similar to calculating your net profit over several days. If you made a profit of $4 on 5 days, $3 on 13 days, and so on, while losing $1 on 2 days and $2 on 17 days, this problem shows you how to calculate your overall profit or loss for the period. This method helps in understanding the overall financial performance by considering both gains and losses.
