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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 x be the number of hours the painter must work to earn at least $200.
The inequality that represents this situation is:
15x ≥ 200
To solve for x, divide both sides of the inequality by 15:
x ≥ 200/15
x ≥ 13.33
Therefore, the minimum number of hours the painter must work to earn at least $200 is 14 hours.
To find the minimum number of hours the painter must work to earn at least $200, we can set up an inequality.
Let's represent the number of hours he works as "h".
Since the painter earns $15 per hour, the total amount he earns can be represented as 15h.
We want to find the minimum number of hours he must work to earn at least $200. So, we set up the inequality:
15h ≥ 200
To solve this inequality, we need to isolate the variable "h" on one side of the inequality symbol.
Divide both sides of the inequality by 15:
(15h)/15 ≥ 200/15
Simplifying the inequality:
h ≥ 40/3
Therefore, the minimum number of hours the painter must work to earn at least $200 is 40/3 hours.
To convert this to a whole number, we can either round it up or take the ceiling value. In this case, since we are looking for the minimum number of hours, we round it up to the next whole number.
Thus, the minimum number of hours the painter must work is 14 hours (rounded up from 40/3).
To solve this problem, we can set up an inequality to represent the situation.
Let x be the number of hours the painter needs to work. We want to find the minimum value of x that satisfies the condition of earning at least $200.
The painter earns $15 per hour, so the total amount he earns in x hours is 15x.
We want this total amount to be at least $200. Therefore, we can write the inequality:
15x ≥ 200
Now let's solve the inequality step-by-step:
1. Divide both sides of the inequality by 15 to isolate x:
(15x) / 15 ≥ 200 / 15
x ≥ 13.33
2. Since the number of hours must be a whole number, we round up to the next whole number:
x ≥ 14
So, the painter must work at least 14 hours to earn at least $200.