Question

4. Christel House Academy has a vegetable garden for students to grow theirown vegetables. They have 300 square feet of garden. Cucumber plantsrequire 6 square feet of growing space, and tomato plants require 4 squarefeet of growing space. The students want to plant some of each type of plantand have at least 60 plants.4. Select ALL the equations or inequalities that could describe thissituation. Let c represent the number of cucumber plants and t representthe number of tomato plants."C>0t<0C + t = 300OOOOOOC +1260bc + 4t53006c + 4 = 300

Answer 1

Given:

The total area of garden is, A = 300 square feet.

The area required for cucumber plants is 6 square feet.

The area required for tomato plants is 4 square feet.

The total number of plants should be at least 60.

The objective is to choose all the correct inequalities.

Step-by-step explanation:

Consider the number of cucumber plants as c and the number of tomato plants as t.

Since, c and t are quantity of plants, it cannot be lesser than zero.

So the correct inequalities are c > 0 and t > 0.

Equation for total number of plants

The equation represents the total number of plants with a sum of at least 60 (greater than or equal to 60) is,

`c+t\ge60`

Equation for total area:

Since, the total area obtained by the students was 300 square feet, the sum of the areas of cucuber and tomato plants should not be more than 300 square feet.

The equation that represents the total area required for cucumber plants and tomato plants can be written as,

`6c+4t\le300`

Thus, the equations matching the correct options are,

`\begin{gathered} c>0 \\ c+t\ge60 \\ 6c+4t\le300 \end{gathered}`

Hence, the correct options are (1), (4) and (5).