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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 "h" represent the number of hours the painter must work.
The amount the painter earns is given by the equation: $15/hour × h(hours) = $15h
We want to find the minimum number of hours the painter must work to earn at least $200, which can be represented by the inequality:
$15h ≥ $200
To isolate the variable "h", divide both sides of the inequality by $15:
h ≥ $200 / $15
Simplifying further:
h ≥ 13.333...
Since the painter cannot work a fraction of an hour, we round up to the next whole number, which is 14.
Therefore, the minimum number of hours the painter must work to earn at least $200 is 14 hours.
To represent this situation using an inequality, we can let x be the number of hours the painter must work. Since the painter earns $15 per hour, the total amount earned for x hours is 15x. The inequality for earning at least $200 can be written as:
15x >= 200
To solve this inequality, we need to isolate x. Divide both sides of the inequality by 15:
15x/15 >= 200/15
x >= 200/15
Now we can calculate the minimum number of hours the painter must work to earn at least $200:
x >= 13.33
The painter must work at least 13.33 hours (or round up to 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 and solve it.
Let's say the number of hours the painter works is represented by 'h'. The amount the painter earns per hour is $15. We want to find the minimum value of 'h' such that the total earnings are at least $200.
The inequality representing this situation can be written as:
15h >= 200
To solve the inequality, we need to isolate 'h' on one side of the inequality sign. To do that, we can divide both sides of the inequality by 15:
15h/15 >= 200/15
Simplifying:
h >= 200/15
Now, we can divide 200 by 15 to find the minimum value of 'h':
h >= 13.33
Since 'h' represents the number of hours the painter works, it can only be a whole number. Therefore, the minimum number of hours the painter must work to earn at least $200 is 14 hours.
To recap:
The inequality to represent the situation is 15h >= 200.
Solving the inequality, we find h >= 13.33.
Since 'h' cannot be a decimal, the minimum number of hours the painter must work is 14 hours.