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Read this word problem. $\newline$ A trout was swimming $9$ feet below the surface of a lake. It dove down $8$ more feet to search for food. What is the position of the trout now relative to the surface? $\newline$ To solve the problem, Denise subtracted $-9 - 8$ and came up with an answer of $-17$ feet. Is Denise correct? Why or why not? $\newline$ Choices: $\newline$ (A)Yes, Denise is correct. $\newline$ (B)No. The answer should have been $17$ feet, not $-17$ feet, because a negative plus a negative is always a positive. $\newline$ (C)No. Denise should have subtracted $8 - 9$ because she needed to find the difference in the trout's starting and ending position.

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Add and subtract integers: word problems

Full solution

Q. Read this word problem.

\newline

A trout was swimming

9

feet below the surface of a lake. It dove down

8

more feet to search for food. What is the position of the trout now relative to the surface?

\newline

To solve the problem, Denise subtracted

-9 - 8

and came up with an answer of

-17

feet. Is Denise correct? Why or why not?

\newline

Choices:

\newline

(A)Yes, Denise is correct.

\newline

(B)No. The answer should have been

17

feet, not

-17

feet, because a negative plus a negative is always a positive.

\newline

(C)No. Denise should have subtracted

8 - 9

because she needed to find the difference in the trout's starting and ending position.

Initial Depth Calculation: The trout was initially $9$ feet below the surface. Diving down $8$ more feet means adding another $8$ feet to the initial $9$ feet below. $\newline$ $-9 + (-8) = -17$ feet.
Incorrect Calculation Explanation: Denise's calculation of $-9 - 8$ is incorrect because when going deeper, we add the depth, not subtract.

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