# Fraction word problem: how many rows are devoted to each plant

• MHB
• skyshooterD
skyshooterD
2. Betty would like your help planning her garden whose rows are all of equal length. She would like to grow carrots, beans, sunflowers, tomatoes and peppers. She tells you she would like to devote twice as many rows to growing peppers as she does to beans. She only has enough tomato plants to occupy one quarter as many rows as she would like to use for pepper plants. She would like to be generous with the number of rows she devotes to her sunflowers, but use only one-sixth of that amount to grow carrots - which is the same as the amount of space she is would like to devote to growing her tomatoes!

(a) Express the number of rows Betty plans on devoting to each plant as a fraction of the total number of rows in the garden.

(b) If Betty’s garden has 21 rows, how many rows are devoted to each plant? Draw a rough sketch to illustrate a plan for such a garden.

Start with the beans, with x (or any other variables you wish) as the number of its rows.

skyshooterD said:
2. Betty would like your help planning her garden whose rows are all of equal length. She would like to grow carrots, beans, sunflowers, tomatoes and peppers. She tells you she would like to devote twice as many rows to growing peppers as she does to beans. She only has enough tomato plants to occupy one quarter as many rows as she would like to use for pepper plants. She would like to be generous with the number of rows she devotes to her sunflowers, but use only one-sixth of that amount to grow carrots - which is the same as the amount of space she is would like to devote to growing her tomatoes!
As always start by naming unknown. Let "c" be the number or rows devoted to growing carrots, "b" the number of rows devoted to beans, "s" the number of rows devoted to sunflowers, "t" the number of rows devoted to growing tomatoes, and "p" the number of rows devoted to growing peppers.

Now translate each piece of information (each sentence) to an equation.
"
she would like to devote twice as many rows to growing peppers as she does to beans" so p= 2b.
"
She only has enough tomato plants to occupy one quarter as many rows as she would like to use for pepper plants" so p= 4t.
"
She would like to be generous with the number of rows she devotes to her sunflowers, but use only one-sixth of that amount to grow carrots" so c= 6s.
"which is the same as the amount of space she is would like to devote to growing her tomatoes!" so c= t

We have the equations p= 2b, p= 4t, c= 6s. and c= t.

(
a) Express the number of rows Betty plans on devoting to each plant as a fraction of the total number of rows in the garden.
Let R be the total number of rows in the garden. Then p+ b+ t+ c+ s= R.
Use the previous equations to reduce that last equation to a single type of plant. For example, from p= 2b, b= p/2 and from p= 4t, t= p/4. c= t= p/4 and s= c/6= p/24 so p+ b+ t+ c+ s= p+ p/2+ p/4+ p/4+ p/24= R. The "least common denominator" is 24: 24p/24+ 12p/24+ 6p/24+ 6p/24+ p/24= 49p/24= R so p= (24/49)R. The number of rows devoted to peppers is 24/49 of the total number of rows in the garden.

Do the same for each of the other plants.

(b) If Betty’s garden has 21 rows, how many rows are devoted to each plant?
Since p= (24/49)R if R= 21 then p= (24/49)(21)= 72/7 which is not a whole number. Check my arithmetic! Or it is possible that this was only meant to be approximate so use 70/7= 10 rows of peppers.
Draw a rough sketch to illustrate a plan for such a garden.

## 1. What is a fraction word problem?

A fraction word problem is a type of mathematical problem that involves using fractions to solve a real-life scenario or situation. It requires understanding of basic fraction concepts such as equivalent fractions, adding, subtracting, multiplying, and dividing fractions.

## 2. How do you solve a fraction word problem?

To solve a fraction word problem, you first need to carefully read and understand the problem. Identify the given information and what is being asked. Then, use the appropriate fraction operation (addition, subtraction, multiplication, or division) to find the solution. Finally, check your answer to ensure it makes sense in the context of the problem.

## 3. What is the importance of understanding fractions in real life?

Understanding fractions is important in real life because it helps us make sense of parts and wholes in everyday situations. For example, when cooking, using fractions allows us to measure and adjust ingredients accurately. In finances, understanding fractions helps us calculate discounts, interest rates, and budgeting. It is also useful in understanding measurements and proportions in fields such as architecture, engineering, and science.

## 4. How can I improve my skills in solving fraction word problems?

To improve your skills in solving fraction word problems, practice is key. Start with simpler problems and gradually move on to more complex ones. Understand the basic concepts of fractions and practice using them in different scenarios. You can also seek help from a teacher, tutor, or online resources for additional guidance and practice problems.

## 5. Can fraction word problems be solved using other methods besides fractions?

Yes, fraction word problems can be solved using other methods such as ratios and proportions. However, understanding fractions is essential in solving these types of problems as they are a fundamental part of ratios and proportions. It is important to have a solid understanding of fractions before moving on to other methods.

• Set Theory, Logic, Probability, Statistics
Replies
45
Views
3K
• Set Theory, Logic, Probability, Statistics
Replies
4
Views
6K
• Precalculus Mathematics Homework Help
Replies
4
Views
2K
• Calculus and Beyond Homework Help
Replies
1
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
5
Views
2K
• Sci-Fi Writing and World Building
Replies
23
Views
8K
• Computing and Technology
Replies
10
Views
2K
• Precalculus Mathematics Homework Help
Replies
2
Views
6K
• Biology and Chemistry Homework Help
Replies
1
Views
3K
• General Discussion
Replies
2
Views
3K