A certain plant grows 1 2/5
inches every week. How long will it take the plant to grow 7 4/5
inches?
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Part 1
How long will it take the plant to grow 7 4/5
inches?
A:6 weeks , 5 days
B: 5 weeks, 3 days
C: 4 weeks, 5 days
D:5 weeks,4 days
To find how long it will take for the plant to grow 7 4/5 inches, we can divide the total growth by the amount the plant grows in one week.
7 4/5 inches / 1 2/5 inches per week = (7 + 4/5) / (1 + 2/5) = (39/5) / (7/5) = (39/5) * (5/7) = 39/7.
Therefore, it will take the plant approximately 5 weeks and 4 days to grow 7 4/5 inches.
The answer is D: 5 weeks, 4 days.
To determine how long it will take the plant to grow 7 4/5 inches, we first need to find out how much the plant grows in one week.
We know that the plant grows 1 2/5 inches every week, which is equivalent to 7/5 inches per week.
Next, we divide the desired growth of 7 4/5 inches by the weekly growth of 7/5 inches to find the number of weeks it will take:
(7 4/5) / (7/5) = (39/5) / (7/5) = (39/5) * (5/7) = 39/7 = 5 4/7.
So, it will take approximately 5 4/7 weeks for the plant to grow 7 4/5 inches.
Now we need to convert this to days. Since there are 7 days in a week, we multiply the fraction part (4/7) by 7 to find the number of days:
(4/7) * 7 = 4.
Therefore, the plant will take 5 weeks and 4 days to grow 7 4/5 inches.
So the correct answer is option D: 5 weeks, 4 days.
To calculate the number of weeks it will take for the plant to grow 7 4/5 inches, we need to divide the total growth by the weekly growth rate.
The weekly growth rate is 1 2/5 inches.
To convert 7 4/5 inches to an improper fraction, we multiply the whole number (7) by the denominator (5), and then add the numerator (4). This gives us 7 * 5 + 4 = 35 + 4 = 39/5 inches.
Now, we divide the total growth of 39/5 inches by the weekly growth rate of 1 2/5 inches.
To divide fractions, we need to multiply the dividend (39/5) by the reciprocal of the divisor (1 2/5). To find the reciprocal of 1 2/5, we flip it, which gives us 5/7.
Now, we multiply: 39/5 * 5/7 = (39 * 5) / (5 * 7) = 195/35.
To simplify the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 5: 195 ÷ 5 / 35 ÷ 5 = 39/7.
Therefore, it will take the plant 39/7 weeks to grow 7 4/5 inches.
Now, we need to convert the improper fraction back to a mixed number. 39 ÷ 7 = 5 remainder 4, so the answer is 5 weeks, 4 days.
Therefore, the correct answer is:
D: 5 weeks, 4 days.