Question

Sarah started 3 miles below the rim of the canyon and hiked until she was 8 miles above the rim. Her brother Sam said she hiked 5 miles. Sarah said she hiked 11 miles.

Who is correct and why?
A. Sam is correct because |3 – 8| = 5.
B. Sam is correct because |–3 – 8| = 5.
C. Sarah is correct because |–3 + 8| = 11.
D. Sarah is correct because |–3 – 8| = 11.

Answer 1

The answer is D

Explanation:

I took the quiz.

Answer 2

D

Explanation:

We can assume that the rim of the canyon is 0. Sarah started 3 miles below, so -3, BUT distance can never be negative, so it's considered 3 miles. Then, she went 8 miles above zero. So the 3 miles she went before reaching the rim plus the 8 miles she went after reaching the rim equals 11 miles.

So now we know that Sarah is right, but how do we know which equation is correct? Well, if we look at option C:

`|-3+8|=11`

When solving absolute value, we solve everything within the absolute value before applying the absolute value. This means that we add -3+8 first, which equals 5, and then apply absolute value, which still equals 5. This equation is not correct.

I hope this helps!