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.
my answer
15h > 200
h > 200/5
h > 13 1/3
1/3(60) = 60/3 = 20
h > 13 1/3
To simplify the fraction 1/3, we can multiply both the numerator and the denominator by 20:
1/3 * 20 = 20/3
So,
h > 13 1/3
can be rewritten as
h > 13 + 20/3
To convert the mixed number into an improper fraction, we multiply the whole number by the denominator and add it to the numerator:
h > 13 + (20/3)
= (39/3) + (20/3)
= 59/3
Therefore, the painter must work at least 59/3 hours, or approximately 19.67 hours, to earn at least $200.
To solve this problem, we set up the following inequality:
15h ≥ 200
To find the minimum number of hours the painter must work, we need to isolate h on one side of the inequality. We can do this by dividing both sides of the inequality by 15:
h ≥ 200/15
Simplifying the right side gives:
h ≥ 40/3
To convert this to a mixed number, we divide 40 by 3:
40 ÷ 3 = 13 1/3
Therefore, the painter must work at least 13 1/3 hours to earn at least $200.
To solve this problem, we need to find the minimum number of hours the painter must work in order to earn at least $200. Let's set up an inequality to represent this situation.
Let h be the number of hours the painter works. Since the painter earns $15 per hour, we can write the inequality:
15h ≥ 200
Now, let's solve for h.
Dividing both sides of the inequality by 15:
h ≥ 200/15
Simplifying the right side:
h ≥ 40/3
To convert the fraction to a mixed number, we divide the numerator (40) by the denominator (3):
40 ÷ 3 = 13 with a remainder of 1
So, 40/3 = 13 1/3.
Therefore, the painter must work at least 13 1/3 hours (or approximately 13 hours and 20 minutes) to earn at least $200.