Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. A painter earns $15 per hour. What is the minimum number of hours he must work to earn at least $200? Write an inequality to represent this situation and solve. Show your work.
Let x represent the number of hours the painter must work.
Since the painter earns $15 per hour, the amount he earns is given by 15x.
We want to find the minimum number of hours he must work to earn at least $200, so we can set up the inequality:
15x ≥ 200
To solve for x, we need to isolate it on one side of the inequality.
Divide both sides of the inequality by 15:
15x/15 ≥ 200/15
x ≥ 200/15
Simplifying, we get:
x ≥ 40/3
So, the painter must work at least 40/3 hours, which can be rounded up to 14 hours or approximately 13.33 hours.
Let's let x represent the number of hours the painter must work.
To calculate the minimum number of hours the painter must work to earn at least $200, we can set up an inequality.
The painter earns $15 per hour, so the amount he earns in x hours is 15x.
We want to find the minimum value of x that satisfies the inequality 15x ≥ 200, where 200 is the minimum amount the painter wants to earn.
To solve for x, we will divide both sides of the inequality by 15.
15x/15 ≥ 200/15
x ≥ 40/3
The painter must work at least 40/3 hours, which is equivalent to 13 and 1/3 hours, to earn at least $200.
To solve this problem, we need to determine the number of hours the painter must work to earn at least $200.
Let's use the variable 'h' to represent the number of hours the painter works.
According to the situation, the painter earns $15 per hour. Therefore, the painter will earn 15h dollars after working 'h' hours.
To find the minimum number of hours required to earn at least $200, we can form the following inequality:
15h ≥ 200
We want to solve this inequality for 'h', so that we get the minimum number of hours.
To solve the inequality, divide both sides by the constant 15:
h ≥ 200 / 15
Simplifying the right side gives:
h ≥ 13.33
Since we are dealing with time, we need to round up to the nearest whole number because the number of hours must be a whole number.
Therefore, the minimum number of hours the painter must work to earn at least $200 is 14 hours.
Explanation:
To solve the problem, we set up an inequality using the wage rate (15 dollars per hour) and the desired minimum earnings ($200). Dividing both sides of the inequality by the wage rate, we find the minimum number of hours required to earn at least $200. Finally, rounding up to the nearest whole number gives us the minimum number of hours the painter must work.