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 be the number of hours the painter must work.
The amount of money the painter earns is given by the formula:
Earnings = Rate * Hours
In this case, the painter earns $15 per hour, so the earnings equation can be written as:
$15x ≥ $200
To solve this inequality for x, we divide both sides of the inequality by 15:
x ≥ 200/15
Simplifying the right side:
x ≥ 40/3
Since we cannot have a fraction of an hour, the painter must work at least 14 hours to earn at least $200.
To find the minimum number of hours the painter must work to earn at least $200, we can set up an inequality.
Let x be the number of hours the painter needs to work.
The painter's earnings can be calculated by multiplying the number of hours worked (x) by the hourly rate ($15), so the inequality becomes:
15x ≥ 200
Now, let's solve the inequality:
15x ≥ 200
Divide both sides of the inequality by 15 to isolate x:
x ≥ 200/15
Evaluate the right side of the equation:
x ≥ 13.333
Since the number of hours worked cannot be fractional, the minimum number of hours the painter must work to earn at least $200 is 14.
So, the painter must work a minimum of 14 hours to earn at least $200.
To solve this problem, we can set up an inequality using the given information. Let's denote the number of hours the painter must work as "h".
The painter earns $15 per hour, so the amount he earns for "h" hours of work would be 15h.
We want to find the minimum number of hours he must work to earn at least $200. This means that the amount he earns, 15h, must be greater than or equal to $200.
So our inequality is:
15h >= 200
To solve for h, we need to isolate it. We can do this by dividing both sides of the inequality by 15. Remember, when dividing or multiplying both sides of an inequality by a negative number, we need to flip the inequality sign. However, since we are dividing by a positive number (15), we don't need to flip the sign.
15h/15 >= 200/15
h >= 200/15
h >= 13.33
Since we're looking for a whole number of hours, we round up to the next whole number.
Therefore, the minimum number of hours the painter must work to earn at least $200 is 14 hours.