Answer :
The cost of one fidget spinner is between 108.34 cents (exclusive) and 109.09 cents (inclusive) based on the given information.
Let's solve this problem step by step.
Step 1: Set up the inequalities.
We are given two inequalities:
1. Eleven fidget spinners cost less than $12, which can be represented as 11x < 1200 cents.
2. Twelve fidget spinners cost more than $13, which can be represented as 12x > 1300 cents.
Where "x" represents the cost of one fidget spinner in cents.
Step 2: Solve the first inequality for "x."
To find the maximum cost of one fidget spinner based on the first inequality, we need to isolate "x":
11x < 1200
Divide both sides by 11:
x < 1200 / 11
x < 109.09 cents (rounded to two decimal places)
So, based on the first inequality, one fidget spinner costs less than 109.09 cents.
Step 3: Solve the second inequality for "x."
To find the minimum cost of one fidget spinner based on the second inequality, we need to isolate "x":
12x > 1300
Divide both sides by 12:
x > 1300 / 12
x > 108.33 cents (rounded to two decimal places)
So, based on the second inequality, one fidget spinner costs more than 108.33 cents.
Step 4: Determine the possible range for the cost of one fidget spinner.
Now, we have two pieces of information:
- One fidget spinner costs less than 109.09 cents (from the first inequality).
- One fidget spinner costs more than 108.33 cents (from the second inequality).
Combining these two pieces of information, we can say that the cost of one fidget spinner is between 108.33 cents (exclusive) and 109.09 cents (inclusive).
So, the cost of one fidget spinner is between 108.34 cents and 109.09 cents.
Final answer:
To find the cost of one fidget spinner, we analyze the inequalities 11x < 1200 cents and 12x > 1300 cents, which gives us the range of 108.33 cents < x < 109.09 cents. Since prices are in whole cents, the fidget spinner likely costs 109 cents each.
Explanation:
To determine the cost of one fidget spinner, we need to analyze the information given. We know that 11 fidget spinners cost less than $12 and 12 fidget spinners cost more than $13. Let's use cents instead of dollars for precision and let x represent the cost of one fidget spinner in cents.
From the first piece of information, we have:
11x < 1200 cents (because $12 is 1200 cents)
From the second piece of information, we have:
12x > 1300 cents (because $13 is 1300 cents)
Dividing the first inequality by 11 gives us x < 109.09 cents, and dividing the second inequality by 12 gives us x > 108.33 cents. Therefore, one fidget spinner costs more than 108.33 cents but less than 109.09 cents. Since we deal with prices in whole cents, the possible cost is 109 cents per fidget spinner, as it is the only whole number in the range given by the inequalities.
