An electrician bought a 100-foot roll of 12-gauge copper wire, and used 32 7/12 feet for one job and 26 3/4 feet for a second job. How many feet of wire remained on the roll?
Group of answer choices
42 2/3 feet
40 2/3 feet
67 5/12 feet
40 7/12 feet
To solve this problem, we first need to determine the total amount of wire used for both jobs. To do this, we add the lengths used for each job:
32 7/12 feet + 26 3/4 feet
To add these fractions, we need to find a common denominator. The least common multiple of 12 and 4 is 12.
Converting the first fraction: 32 7/12 = 384/12 + 7/12 = 391/12
Converting the second fraction: 26 3/4 = 26/4 + 3/4 = 29/4
Now, we can add the fractions:
391/12 + 29/4
To add these fractions, they need a common denominator of 12. Since 4 can be multiplied by 3 to get 12, we multiply both the numerator and denominator of the second fraction by 3:
391/12 + (29/4)*(3/3) = 391/12 + 87/12 = 478/12
Now we can simplify the fraction:
478/12 = 39 10/12 = 39 5/6
So, a total of 39 5/6 feet of wire were used for both jobs.
To find how much wire remained on the roll, we subtract the total amount used from the initial amount bought:
100 feet - 39 5/6 feet
Converting 39 5/6 to an improper fraction: 39 5/6 = (6*39 + 5)/6 = 239/6
Now, we can subtract the fractions:
100 feet - 239/6 feet
To subtract fractions, they need a common denominator of 6. Since 6 is already the denominator of the second fraction, we don't need to make any adjustments.
Rewriting 100 as a fraction with a denominator of 6:
100 feet = (100/1)*(6/6) = 600/6
Now we can subtract the fractions:
600/6 - 239/6 = (600 - 239)/6 = 361/6
Converting the fraction to a mixed number:
361/6 = 60 1/6
Therefore, 60 1/6 feet of wire remained on the roll.
The correct answer is: 60 1/6 feet