An inequality that represents the number of each type of molecular set the school can buy is y ≤ 50 - 23x/12, which is shown in the graph attached below.
Assuming the school decides to buy 20 of the large kits, the number of small kit that can be bought now is 11 small kits.
How to write and solve the system of inequalities graphically?
In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of large kit and number of small kit purchased, and then translate the word problem into algebraic equation as follows:
- Let the variable x represent the number of large kit purchased.
- Let the variable y represent the number of small kit purchased.
Since each large kit cost $23 and each small kit costs $12, and this school has only $600 to buy molecular sets for students we have;
23x + 12y ≤ 600
Next, we would solve for y from the equation above;
12y ≤ 600 - 23x
y ≤ 600/12 - 23x/12
y ≤ 50 - 23x/12.
Assuming the school decides to buy 20 of the large kits, an inequality to represent this situation is given by;
23(20) + 12y ≤ 600
460 + 12y ≤ 600
12y ≤ 600 - 460
y ≤ 600/12 - 460/12
y ≤ 50 - 38.333
y ≤ 11.667.
Therefore, the school can only purchase 11 small kits when it decides to buy 20 of the large kits.
Read more on inequality here: brainly.com/question/28748540
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