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Read this word problem. $\newline$ When Emmett began his science experiment, he had $20$ milliliters of an unknown solution. During the experiment, the change in the volume of the solution was $-9$ milliliters. What was the final volume of the solution? $\newline$ To solve the problem, Dakota added $20 + (-9)$ and came up with an answer of $-11$ milliliters. Is Dakota correct? Why or why not? $\newline$ Choices: $\newline$ (A)Yes, Dakota is correct. $\newline$ (B)No. The answer should have been $11$ milliliters, not $-11$ milliliters, because the volume should not be negative. $\newline$ (C)No. Dakota should have subtracted $20 - (-9)$ because the volume decreased.

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Add and subtract integers: word problems

Full solution

Q. Read this word problem.

\newline

When Emmett began his science experiment, he had

20

milliliters of an unknown solution. During the experiment, the change in the volume of the solution was

-9

milliliters. What was the final volume of the solution?

\newline

To solve the problem, Dakota added

20 + (-9)

and came up with an answer of

-11

milliliters. Is Dakota correct? Why or why not?

\newline

Choices:

\newline

(A)Yes, Dakota is correct.

\newline

(B)No. The answer should have been

11

milliliters, not

-11

milliliters, because the volume should not be negative.

\newline

(C)No. Dakota should have subtracted

20 - (-9)

because the volume decreased.

Initial Volume: Dakota started with the initial volume of the solution which was $20$ milliliters.
Add Change in Volume: Then, Dakota added the change in volume, which was $-9$ milliliters, to the initial volume. So, $20 + (-9)$ .
Calculate New Volume: Adding $20$ and $-9$ gives us $20 - 9$ , which equals $11$ milliliters.
Correct Answer: Dakota's answer was $-11$ milliliters, but since we can't have a negative volume of a solution, the correct answer should be $11$ milliliters.

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