A hike starts at an elevation of 13 and four-fifths feet below sea level and ends at an elevation that is 1,542 feet higher. How high is the hiker, in feet, above sea level at the end of the hike?
A. 1,528
B. 1,528 and one-fifth
C. 1,555
D. 1,555 and four-fifths
Starting at an elevation of 13 and four-fifths feet below sea level, we can represent this as -13 4/5 feet.
The hike ends at an elevation that is 1,542 feet higher, so we add 1,542 to -13 4/5.
To add these numbers, we first convert -13 4/5 to a fraction: -13 4/5 = - (13 * 5 + 4)/5 = - 69/5.
Now we can add the fractions: -69/5 + 1,542 = -69/5 + 7,710/5 = (7,710 - 69)/5 = 7,641/5.
To convert this fraction back to a mixed number, we divide the numerator (7,641) by the denominator (5): 7,641 ÷ 5 = 1,528 remainder 1.
Therefore, the hiker is at an elevation of 1,528 and one-fifth feet above sea level at the end of the hike.
The answer is B. 1,528 and one-fifth.