If you need to show Greater-than or Equal-to, use ">=" If you need to show Less-than or Equal-to, use "<=" If you need to show Not Equal-to, use "=/" 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.

Question

If you need to show Greater-than or Equal-to, use ">=" If you need to show Less-than or Equal-to, use "<=" If you need to show Not Equal-to, use "=/" 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.

Answer 1

Let's call the number of hours the painter must work "x".

According to the problem, the painter earns $15 per hour. So, the amount he earns after working "x" hours is 15x.
The problem states that he must earn at least $200. We can write this as an inequality:
15x ≥ 200.
To solve this inequality, we need to isolate the variable "x". We can do this by dividing both sides of the inequality by 15:
x ≥ 200/15.
Dividing 200 by 15, we get:
x ≥ 13.33.
Since the number of hours must be an integer (since you can't work a fraction of an hour), the minimum number of hours the painter must work is 14 hours.

Answer 2

To represent this situation with an inequality, we can let "x" represent the number of hours the painter must work.

Since the painter earns $15 per hour, the painter's total earnings can be calculated by multiplying the hourly rate by the number of hours worked: 15x.

Now, we want to find the minimum number of hours the painter must work to earn at least $200.

So, we can write the inequality: 15x >= 200.

To solve this inequality, we need to isolate the variable "x".

First, divide both sides of the inequality by 15: (15x)/15 >= 200/15.

Simplifying: x >= 200/15.

Now, let's calculate the minimum number of hours using this inequality:

x >= 200/15 = 13.33.

Since the number of hours worked must be a whole number, the painter must work at least 14 hours to earn a minimum of $200.

Answer 3

To find the minimum number of hours the painter must work to earn at least $200, we can set up an inequality.

Let's assume 'x' represents the number of hours the painter works. The amount the painter earns can be calculated by multiplying the number of hours worked, 'x', by the hourly rate of $15. So the amount the painter earns is 15x.

We want to find the minimum number of hours (x) that satisfies the condition "earn at least $200."

To represent this condition, we use the inequality symbol ">=" (Greater-than or Equal-to).

The inequality can be written as:

15x >= 200

Now let's solve this inequality to find the minimum value for 'x.'

Divide both sides of the equation by 15 to isolate 'x.'

(15x)/15 >= 200/15

Simplifying, we have:

x >= 200/15

x >= 13.33

Since the number of hours cannot be fractional, we round up to the next whole number to find the minimum value for 'x.' Therefore, the painter must work a minimum of 14 hours to earn at least $200.