Alice worked 40 hours at regular pay and 52/3 hours at 11/2 pay. How many hours will Alice be paid for in total?
Alice will be paid for 45 2/3 hours in total.
To find out how many hours Alice will be paid for in total, we can add the hours worked at regular pay to the hours worked at 11/2 pay.
First, let's calculate the total hours worked at regular pay. Alice worked 40 hours at regular pay.
Next, let's calculate the total hours worked at 11/2 pay. We can convert the mixed number 52/3 to an improper fraction. To do this, we multiply the whole number (5) by the denominator (3) and add the numerator (2). So, 52/3 can be converted to (3*5+2)/3 = 17/3. This means Alice worked 17/3 hours at 11/2 pay.
Now, we can add the hours worked at regular pay (40 hours) to the hours worked at 11/2 pay (17/3 hours). To add these fractions, we need a common denominator. The least common multiple of 3 and 1 is 3. So, we can rewrite 40 hours as 40/1 = (40*3)/3 = 120/3.
Now we can add the fractions: 120/3 + 17/3 = (120 + 17)/3 = 137/3.
Therefore, Alice will be paid for a total of 137/3 hours.
To find out the total number of hours that Alice will be paid for, we need to add the hours worked at regular pay and the hours worked at 11/2 pay.
1. Alice worked 40 hours at regular pay.
2. Alice worked 52/3 hours at 11/2 pay.
To simplify the second part, we can convert 52/3 to a mixed number:
- Divide the numerator (52) by the denominator (3): 52 รท 3 = 17 with a remainder of 1/3.
- The mixed number is 17 1/3.
Now we can add the hours together:
40 hours + 17 1/3 hours.
To add these, we need to convert 1/3 to a fraction with a denominator of 3:
1/3 = 1 * 3/3 = 3/3.
Now we can add the hours:
40 hours + 17 1/3 hours = 40 hours + 17 hours + 3/3 hours.
Adding the whole numbers:
40 hours + 17 hours = 57 hours.
Adding the fractions:
3/3 hours is equal to 1 hour.
So, the total number of hours Alice will be paid for is 57 hours + 1 hour = 58 hours.