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Four players are playing a game together. They each gain or lose points based on their actions.
Amani gains 50 points for finding a green mushroom.
Ajeet gains 100 points for completing a level.
Damian loses 100 points for getting hit by a fireball.
Julius loses 75 points for stepping on a spike.
Which two friends had the same amount of change to their scores?
Choose 1 answer:
(A) Amani and Ajeet
(B) Damian and Julius
(c) Amani and Julius
(D) Ajeet and Damian

Four players are playing a game together. They each gain or lose points based on their actions. $\newline$ Amani gains $50$ points for finding a green mushroom. $\newline$ Ajeet gains $100$ points for completing a level. $\newline$ Damian loses $100$ points for getting hit by a fireball. $\newline$ Julius loses $75$ points for stepping on a spike. $\newline$ Which two friends had the same amount of change to their scores? $\newline$ Choose $1$ answer: $\newline$ (A) Amani and Ajeet $\newline$ (B) Damian and Julius $\newline$ (C) Amani and Julius $\newline$ (D) Ajeet and Damian

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Quantities that combine to zero: word problems

Full solution

Q. Four players are playing a game together. They each gain or lose points based on their actions.

\newline

Amani gains

50

points for finding a green mushroom.

\newline

Ajeet gains

100

points for completing a level.

\newline

Damian loses

100

points for getting hit by a fireball.

\newline

Julius loses

75

points for stepping on a spike.

\newline

Which two friends had the same amount of change to their scores?

\newline

Choose

1

answer:

\newline

(A) Amani and Ajeet

\newline

(B) Damian and Julius

\newline

(C) Amani and Julius

\newline

(D) Ajeet and Damian

Calculate Amani's point change: Calculate the change in points for Amani. Amani gains $50$ points.
Calculate Ajeet's point change: Calculate the change in points for Ajeet. $\newline$ Ajeet gains $100$ points.
Calculate Damian's point change: Calculate the change in points for Damian. $\newline$ Damian loses $100$ points, which is a change of $-100$ points.
Calculate Julius's point change: Calculate the change in points for Julius. Julius loses $75$ points, which is a change of $-75$ points.
Compare point changes of friends: Compare the changes in points to find two friends with the same amount of change. Amani has $+50$ points, Ajeet has $+100$ points, Damian has $-100$ points, and Julius has $-75$ points. The only two friends with the same amount of change are Damian and Julius, both of whom have negative changes in their scores.

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