Fraction word problem

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Jacob Lee

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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.
 
Jacob Lee 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!

(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.
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https://www.freemathhelp.com/forum/threads/read-before-posting.109846/

Please share your work/thoughts and context of the problem (what is the subject topic?) - so that we know where to begin to help you.
 
There are several ways you might attack this, but here is one way to start:

Define a variable representing the number of rows of each plant. For example, C = number of rows of carrots, B = number of rows of beans, and so on.

Then write an equation representing each thing you are told; for example, the number of rows of peppers is twice as many as the rows of beans, so P = 2B.

Then, see what you can do to solve the equations. It's implied that there is not enough information yet to determine the actual numbers, but you should able to solve for ratios, or something like that. Or, you might define an extra variable R for the total number of rows, and write an equation for that fact; then you should be able to solve for everything in terms of R.

Now show us what you can do, as we've asked. Also, tell us what topic this problem came under; that may give us a clue as to what method you are expected to use.
 
This problem is a duplicate one on this forum posted yesterday.
 
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