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Answer :
Using a system of linear equations, we determine that it takes Katrina 2 hours to make one bracelet and 4 hours to make one necklace by solving the equations derived from her work hours over two weeks.
The question involves solving a system of linear equations to determine how many hours it takes Katrina to make one bracelet and one necklace. Let's assign variables to represent the time per item: let B be the time to make a bracelet and N be the time to make a necklace. From the information given, we can set up the following equations based on the 16 hours of work each week:
- 4B + 2N = 16 (last week)
- 2B + 3N = 16 (this week)
To solve these equations, we can use the method of substitution or elimination. For this solution, we'll use the elimination method. Multiply the first equation by 3 and the second by 2 to eliminate N:
- 12B + 6N = 48
- 4B + 6N = 32
Subtract the second equation from the first:
- 8B = 16
Divide both sides by 8 to find B:
- B = 2
Now we know it takes 2 hours to make one bracelet. Insert B into one of the original equations to find N:
- 4(2) + 2N = 16
- 8 + 2N = 16
- 2N = 8
- N = 4
It takes Katrina 4 hours to make one necklace. Therefore, the time to make one bracelet is 2 hours and the time to make one necklace is 4 hours.
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