A landscaper is planning a public garden. She uses the diagram to decide on the number of ash trees to plant, based on garden size in acres.

Question

Diagram of trees, with 8 trees corresponding with one-eighth of an acre.

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Based on this proportional relationship, the landscaper will plant _[blank 1]_ trees per acre of land. If the garden covers 78
of an acre, she can use the equation _[blank 2]_ to determine t,
the number of trees to plant, based on g,
the size of the garden in acres.

Select two answers: one for blank 1 and one for blank 2.

Responses

blank 1: 80
blank 1: 80

blank 2: t=64g
blank 2: t is equal to 64 g

blank 1: 8
blank 1: 8

blank 1: 64
blank 1: 64

blank 2: t=78g
blank 2: t is equal to 7 eighths g

blank 2: t=8g
blank 2: t is equal to 8 g

blank 1: 56
blank 1: 56

blank 2: t=18g

Answer 1

To determine how many trees the landscaper will plant per acre of land and the equation to use based on the garden size in acres, we can analyze the given information:

• The diagram indicates that there are 8 trees for one-eighth of an acre. To find out how many trees correspond to 1 acre, we multiply 8 by 8 (since 1 acre is 8 times larger than one-eighth of an acre):

  \( 8 \text{ trees} \times 8 = 64 \text{ trees per acre} \)

So, for blank 1, the answer is:

blank 1: 64

Next, to establish a formula for the number of trees \( t \) based on \( g \), the size of the garden in acres, we can set up a proportion:

Since there are 64 trees per acre, the formula will be:

\( t = 64g \)

Thus, for blank 2, the answer is:

blank 2: t = 64g

Final answers:

• Blank 1: 64
• Blank 2: t = 64g