i)
You are trying to decide if it is worth the investment to make the cakes if it takes 2.5 hours to make each cake and you have 200 hours this summer to devote to creating your product. Write an inequality that represents your time constraint.
*Use x as the variable
You can copy and paste the inequality sign below in your answer.
≥ < > ≤
*
1 point
2.5x ≤ 200
j)
Solve your inequality from part i
*
To solve the inequality 2.5x ≤ 200, we need to divide both sides of the inequality by 2.5 to isolate the variable x:
2.5x ≤ 200
x ≤ 200 / 2.5
Simplifying the right side:
x ≤ 80
So the solution to the inequality is x ≤ 80.
To solve the inequality 2.5x ≤ 200:
1. First, divide both sides of the inequality by 2.5 to isolate the variable x:
(2.5x) / 2.5 ≤ 200 / 2.5
This simplifies to:
x ≤ 80
So, the solution to the inequality is x ≤ 80.
To answer part i), we need to represent the time constraint using an inequality. Since each cake takes 2.5 hours to make, and we have a total of 200 hours, we can use the inequality ≤ (less than or equal to) to represent this.
The variable x represents the number of cakes we make. So, the inequality representing the time constraint is:
2.5x ≤ 200
Now, to solve this inequality from part i), we need to find the value of x that satisfies the inequality. To do this, we divide both sides of the inequality by 2.5:
2.5x / 2.5 ≤ 200 / 2.5
Simplifying this, we get:
x ≤ 80
Therefore, the solution to the inequality 2.5x ≤ 200 is x ≤ 80. This means that you can make a maximum of 80 cakes within the given time constraint of 200 hours.