A worker was paid $218 for each day he worked and was fined $36 each day he was absent. at the end of 30 days he earned $5524. how many days he was absent?
218x - 36(30-x) = 5524
Well, it looks like this worker had a bit of a love-hate relationship with their job! Let's do some math to figure out how many days they were absent.
Let's assume the worker was absent for x number of days. Now, let's calculate their earnings and fines.
Since the worker earned $218 for each day they worked, their earnings would be 218 * (30 - x).
Similarly, since they were fined $36 for each day they were absent, their fines would total 36x.
Now, we can set up an equation to represent the situation:
Earnings - Fines = Total earnings
218 * (30 - x) - 36x = 5524
Now, let's solve the equation and find the value of x.
218 * 30 - 218x - 36x = 5524
6540 - 254x = 5524
-254x = 5524 - 6540
-254x = -1016
x = (-1016) / (-254)
x = 4
So, the worker was absent for 4 days. I hope he had a good reason for being absent, like a clown convention or a surprise party!
Let's break down the problem step-by-step:
Let's assume the worker was absent for "x" days.
The worker was paid $218 for each day he worked. So, he earned $218 * (30 - x) for the days he worked.
The worker was fined $36 for each day he was absent. So, he was fined $36 * x for the days he was absent.
The total amount the worker earned after 30 days is $5524.
So, we can write the equation: $218 * (30 - x) - $36 * x = $5524
Now, let's solve for "x":
$218 * 30 - $218 * x - $36 * x = $5524
$6540 - $218x - $36x = $5524
Simplifying the equation:
- $254x = $5524 - $6540
- $254x = - $1016
Dividing both sides by - $254:
x = (- $1016) / (- $254)
x = 4
Therefore, the worker was absent for 4 days.
To find the number of days the worker was absent, we can use algebraic equations. Let's assume the worker was absent for 'x' days.
Since the worker was paid $218 for each day he worked and fined $36 for each day he was absent, we can create the following equations:
Number of days worked: 30 - x
Payment for days worked: ($218) * (number of days worked) = $218 * (30 - x)
Fine for days absent: ($36) * (number of days absent) = $36 * x
The total amount earned at the end of 30 days is given as $5524. Therefore, we can set up the equation:
Total amount earned = Payment for days worked - Fine for days absent
$5524 = $218 * (30 - x) - $36 * x
Now, let's solve this equation to find the value of 'x' (number of days absent):
$5524 = $218 * 30 - $218 * x - $36 * x
$5524 = $6540 - $254 * x - $36 * x
$254 * x + $36 * x = $6540 - $5524
$290 * x = $1016
Dividing both sides by $290:
x = $1016 / $290
Evaluating the right side of the equation:
x ≈ 3.5
Since x represents the number of days, we cannot have a fraction of a day. Thus, the worker was absent for approximately 3 days.