Final answer:
To find when Bryan's snowman will be less than 2 1/2 feet tall, we convert all measurements to improper fractions, calculate the snowman's height change per day, and solve for the number of days. The snowman will be below the desired height after 5 3/5 days.
Step-by-step explanation:
The student asked when a snowman that starts at a height of 4 5/6 feet tall and decreases in height by −5/12 foot per day will be less than 2 1/2 feet tall. To solve this, we first convert the mixed numbers to improper fractions: 4 5/6 feet becomes 29/6 feet and 2 1/2 feet becomes 5/2 feet. Then, we set up an equation to calculate the height of the snowman after x days, which is 29/6 - (5/12)x, and solve for x to be the day when the height is less than 5/2 feet.
First, we find a common denominator for the fractions, which is 12, to combine them. The equation becomes:
(29/6) x (2/2) - (5/12)x < (5/2) x (6/6)
58/12 - (5/12)x < 15/6 x (2/2)
58/12 - (5/12)x < 30/12
Subtract 58/12 from both sides to get:
-(5/12)x < -28/12
Since we are dividing by a negative number, the inequality sign changes direction when we divide both sides by -5/12:
x > 28/5
Converting 28/5 into a mixed number gives us 5 3/5 days. Thus, the snowman will be less than 2 1/2 feet tall after 5 3/5 days, which is partway through the sixth day.