can someone please help me to writ an inequality for this wor problem? Mr.Kirkland receives $13/hr. for regular time (8hr./day) and double pay for working on holidays. He worked on Friday even though it was a holiday. If his week's pay was at least $650, how many hours did he work on Friday?
Assuming he worked 4 full days, and x hours on Friday (the holiday), then
13*8*4 + 26x >= 650
Ah, Mr. Kirkland, the dedicated holiday worker! Let me whip up an inequality for you to solve this little riddle.
Let's call the number of hours Mr. Kirkland worked on Friday "x." Now, let's break it down:
On regular days, Mr. Kirkland earns $13 per hour, so he earned 13 * 8 = $104 for a regular day.
On holidays, though, he earns twice that amount, so he earned 2 * 13 * x = $26x on Friday.
So, his total pay for the week is $650.
Now, let's put it all together:
104 (regular pay) + 26x (holiday pay) ≥ 650
And that's the inequality! Now, solve for x and find out how many hours Mr. Kirkland worked on that fateful holiday Friday.
Let's denote the number of hours Mr. Kirkland worked on Friday as "x".
Since he worked 8 hours per day for the rest of the week, we can calculate his regular pay as follows:
Regular pay = $13/hr. * 8 hrs./day * 4 days = $416
As he received double pay for working on Friday, his additional pay for that day would be:
Double pay = ($13/hr. * 2) * x hrs.
His total pay for the week would be his regular pay plus his additional pay for working on Friday:
Total pay = Regular pay + Double pay
According to the problem, his total pay must be at least $650. Thus, we can set up the inequality:
Total pay >= $650
Substituting the expressions we found, we get:
$416 + ($13/hr. * 2) * x hrs. >= $650
Now we can solve this inequality to find the possible values of x.
To write an inequality for this word problem, we can start by determining the amount Mr. Kirkland earned for regular time and holiday time separately.
For regular time (8 hours/day) at a rate of $13/hr, Mr. Kirkland earns $13 x 8 = $104 per day.
For working on a holiday, he earns double his regular rate, which is $13 x 2 = $26 per hour.
Let's assume Mr. Kirkland worked "x" hours on Friday. Since Friday was a holiday, he earned $26 per hour for those hours.
To calculate his total pay for the week, we need to consider his regular time and holiday time together. His regular pay for 5 days is $104 x 5 = $520.
Since his week's pay was at least $650, we can write the inequality:
Regular pay + Holiday pay ≥ Total pay for the week
$520 + ($26 * x) ≥ $650
Now we can solve the inequality to find the value of "x" (the hours worked on Friday).
$520 + $26x ≥ $650
Subtracting $520 from both sides:
$26x ≥ $650 - $520
$26x ≥ $130
To isolate "x", divide both sides by $26:
x ≥ $130 / $26
x ≥ 5
Therefore, Mr. Kirkland must have worked at least 5 hours on Friday to earn a week's pay of at least $650.