Word problem!

[Jacob Lee]

I am completely lost and I am not sure what to do for this problem.


"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.

 

[lev888]

Let's use the first letters for variable names: C, B, S, T, P - numbers of rows for the corresponding plant.

1. Express what we know through variables:
"she would like to devote twice as many rows to growing peppers as she does to beans" means P = 2*B
"enough tomato plants to occupy one quarter as many rows as she would like to use for pepper plants" means T = P/4
"use only one-sixth of that amount (sunflowers) to grow carrots" means C = S/6
"which is the same as the amount of space she is would like to devote to growing her tomatoes" means C = T

2. Eliminate variables. Pick one and use it for all plants. How about T?
C = T, easy enough
S = 6C = 6T
P = ?
B = ?

3. Now we can add them all up to get the total number of rows as function of T: ?
4. Fraction of rows: divide what you found in step 2 by the total
5. If the total is 21 rows and you know the fractions for each plant you can get number of rows for each plant.

 

[Steven G]

she would like to devote twice as many rows to growing peppers as she does to beans
So we are comparing peppers to BEANS.
So let B= # of rows or beans
And 2B = # of rows for peppers

She only has enough tomato plants to occupy one quarter as many rows as she would like to use for pepper plants
The number of rows of peppers is already known to be 2B (see above)
Then the # of rows for tomatoes = (1/4)(2B) = B/2

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
The number of rows of carrots = B/2
The number of rows of sunflower = 6(number of rows of carrots) = 6(B/2)= 3B

Continue from here.

 

[Jacob Lee]

Let's use the first letters for variable names: C, B, S, T, P - numbers of rows for the corresponding plant.

1. Express what we know through variables:
"she would like to devote twice as many rows to growing peppers as she does to beans" means P = 2*B
"enough tomato plants to occupy one quarter as many rows as she would like to use for pepper plants" means T = P/4
"use only one-sixth of that amount (sunflowers) to grow carrots" means C = S/6
"which is the same as the amount of space she is would like to devote to growing her tomatoes" means C = T

2. Eliminate variables. Pick one and use it for all plants. How about T?
C = T, easy enough
S = 6C = 6T
P = ?
B = ?

3. Now we can add them all up to get the total number of rows as function of T: ?
4. Fraction of rows: divide what you found in step 2 by the total
5. If the total is 21 rows and you know the fractions for each plant you can get number of rows for each plant.

I am still kind of confused on how to isolate the variables.

 

[lev888]

I am still kind of confused on how to isolate the variables.

Isolate? Second step?

 

[Deleted member 4993]

I am still kind of confused on how to isolate the variables.

Isolate variables from where - equation?