A rope is rated to hold 21 2/5 pounds before it breaks.Estimate by rounding to the nearest pound how many 2 5/8 pound weights the rope will hold ?
A. 2 32/39
B. 3/10
C.10 5/24
D. 3 1/3
None are rounded to the nearest pound.
However, unless there are typos, the closest answer would be C, since I estimate 21/3 = 7.
To answer this question, we need to calculate how many whole 2 5/8 pound weights the rope can hold.
First, let's convert the mixed number 2 5/8 into an improper fraction.
The improper fraction equivalent of 2 5/8 is (8 * 2 + 5) / 8 = 21/8.
Next, divide the rated weight of the rope (21 2/5 pounds) by the weight of one 2 5/8 pound weight (21/8 pounds):
(21 2/5) / (21/8)
To divide fractions, we invert the divisor and multiply:
(21 2/5) * (8/21)
Now, let's calculate the result:
(21*8 + 2) / (5*21)
(168 + 2) / 105
170 / 105
= 1 65/105
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 5:
(1*5 + 65/5) / (105/5)
(5 + 13) / 21
18 / 21
Now we round this result to the nearest whole number (pound) to estimate how many 2 5/8 pound weights the rope will hold.
To round 18/21 to the nearest whole number, we will check if the numerator is greater than or equal to half the denominator. In this case, 18 is greater than half of 21 (which is 10.5).
Therefore, the rope will hold 3 whole 2 5/8 pound weights since the numerator is greater than half the denominator.
The correct answer is D. 3 1/3.