The gardening club at school is growing vegetables. The club has 300 square feet of planting beds. Cucumber plants require 6 square feet of growing space, and tomato plants require 4 square feet of growing space. The students want to plant some of each type of plant and have at least 60 plants.

The express relations between expressions with a sign other than the equal sign. Common relationals are 'less than', 'greater than', 'not equal to', and many others.

The gardening club at school has 300 square feet of planting beds to plant cucumber and tomato. Each cucumber plant requires 6 square feet of growing space and each tomato plant requires 4 square feet of growing space. We know the total area cannot exceed 300 square feet, so

[tex]6c+4t\leq 300[/tex]

Being c and t the number of cucumber and tomato plants respectively.

We also know the students want to plant some of each type of plant and have at least 60 plants. This lead us to more conditions

[tex]c>0\\t > 0\\c+t\geq 60[/tex]

Note: The set of inequalities shown is not enough to uniquely solve the problem. We need something to maximize or minimize to optimize c and t

fichoh fichoh · Answer 2 · 2021-10-11T11:45:43+02:00

The system of inequalities which represents the scenario described are ::

t + c ≥ 60

6c + 4t ≤ 300

Total planting area = 300 ft²

Required area for cucumber = 6 ft²

Required area for tomato = 4 ft²

Let ;

Number of cucumber = c
Number of tomatoes = t

Therefore, the system of inequalities can be expressed thus :

Total Number of plants = tomato + cucumber ≥ 60

t + c ≥ 60

Total planting area :

6c + 4t ≤ 300

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