Question

A certain plant grows \[1\dfrac{3}{4}\] inches every week. how long will it take the plant to grow \[10\dfrac{1}{4}\] inches?

Answer 1

Hint: Here in this question, we have to find the how many days or week does the plant take to grow \[10\dfrac{1}{4}\] inches. This problem is based on the concept of ratio and proportion. Given how much the plant has grown for one week by using this we can find the required days which plant has grown \[10\dfrac{1}{4}\] inches. By using the basic arithmetic operation.

Complete step-by-step answer:
The question is a word question. We read the question and we write the data from the question.
Consider the given data in question
A certain plant grows \[1\dfrac{1}{4}\] inches for one week. now we convert the mixed fraction into an improper fraction. so we have \[\dfrac{5}{4}\] inches.
Therefore, the plant grows for each day = \[\dfrac{{\dfrac{5}{4}\,inches}}{{7\,days}}\]
Here, we have to find the how long the plant takes to grow \[10\dfrac{1}{4}\] inches
Let us take
The days will be taken by the plant to grow \[10\dfrac{1}{4}\] inches = d days
This can be written as
The plant grows \[10\dfrac{1}{4}\] inches = \[\dfrac{{10\dfrac{1}{4}\,inches}}{{d\,days}}\] = \[\dfrac{{\dfrac{{41}}{4}\,inches}}{{d\,days}}\]
Basically, it is a ratio and proportion problem
Then consider the two ratios and we equate the both ratios and then it is written as
 \[ \Rightarrow \dfrac{{\dfrac{5}{4}\,inches}}{{7\,days}} = \dfrac{{\dfrac{{41}}{4}\,inches}}{{d\,days}}\]
On cross multiplication, we have
 \[ \Rightarrow \dfrac{5}{4} \times d = \dfrac{{41}}{4} \times 7\]
On multiplication, we get
 \[ \Rightarrow 5d = 287\]
On dividing by 5.
 \[ \Rightarrow d = 37\dfrac{2}{5}\] days.
Hence, the plant grows \[10\dfrac{1}{4}\] inches, it will take \[37\dfrac{2}{5}\] days.
So, the correct answer is “ \[37\dfrac{2}{5}\] ”.

Note: Here in this we use the simple trick. We write the given data and then we use the cross multiplication. Then we use the simple multiplication. While multiplication or multiplying the numbers, we must know the table of multiplication. Hence, we determine the result for the given question.