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Amy hikes down a slope to a lake that is 10.2 meters below the trail. Then Amy jumps into the lake, and swims 1.5 meters down. She wonders what her new height is relative to the trail.
Which of the following equations matches the situation above?
Choose 1 answer:
(A)
-10.2+1.5= ?
(B)
10.2-1.5=?
(c)
-10.2-1.5= ?

Amy hikes down a slope to a lake that is $10$ . $2$ meters below the trail. Then Amy jumps into the lake, and swims $1$ . $5$ meters down. She wonders what her new height is relative to the trail. $\newline$ Which of the following equations matches the situation above? $\newline$ Choose $1$ answer: $\newline$ (A) $-10.2+1.5=$ ? $\newline$ (B) $10.2-1.5=$ ? $\newline$ (C) $-10.2-1.5=$ ?

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Solve a system of equations using any method: word problems

Full solution

Q. Amy hikes down a slope to a lake that is

10

.

2

meters below the trail. Then Amy jumps into the lake, and swims

1

.

5

meters down. She wonders what her new height is relative to the trail.

\newline

Which of the following equations matches the situation above?

\newline

Choose

1

answer:

\newline

(A)

-10.2+1.5=

?

\newline

(B)

10.2-1.5=

?

\newline

(C)

-10.2-1.5=

?

Start at Trail: Amy starts at the trail and then moves down to the lake, which is $10.2$ meters below the trail. To represent this downward movement, we use a negative number because she is moving below the starting point. So, the change in height when she reaches the lake is $-10.2$ meters.
Move to Lake: After reaching the lake, Amy jumps in and swims down an additional $1.5$ meters. Since she is moving further down from the lake's surface, this is also a negative change in height relative to the lake. Therefore, we add another negative number, $-1.5$ meters, to represent this additional downward movement.
Swim Down Further: To find Amy's new height relative to the trail after both movements, we need to add the two changes in height together. Since both movements are downward (below the trail), we add the two negative numbers: $-10.2$ meters (from trail to lake) and $-1.5$ meters (from lake surface further down).
Calculate New Height: The correct equation to represent the situation is therefore: $-10.2$ meters (height change to the lake) $- 1.5$ meters (additional height change swimming down) equals Amy's new height relative to the trail. This corresponds to option (C) $-10.2 - 1.5 = ?$
Perform Calculation: Now we perform the calculation: $-10.2 - 1.5 = -11.7$ . Amy's new height relative to the trail is $-11.7$ meters, which means she is $11.7$ meters below the point where the trail is located.

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