Answer :
Final answer:
It takes Katrina 3 hours to make one bracelet and 4 hours to make one necklace. We found this by setting up a system of equations based on the time taken to produce bracelets and necklaces during two different weeks and then solving the equations simultaneously.
Explanation:
To solve this problem, we'll use a system of equations to find how many hours it takes Katrina to make one bracelet and one necklace. We have two scenarios:
- 5 bracelets and 3 necklaces take 27 hours to make.
- 2 bracelets and 4 necklaces take 22 hours to make.
Let B represent the number of hours to make one bracelet and N represent the number of hours to make one necklace. We can set up the following system of equations based on the information given:
- 5B + 3N = 27
- 2B + 4N = 22
Solving these equations simultaneously, we multiply the first equation by 2 and the second by 5, to eliminate B:
- 10B + 6N = 54 (multiply first equation by 2)
- 10B + 20N = 110 (multiply second equation by 5)
Subtract the first new equation from the second to eliminate B:
- 10B + 20N - (10B + 6N) = 110 - 54
- 14N = 56
- N = 56 / 14
- N = 4
Now use the value of N to find B using one of the original equations:
- 5B + 3(4) = 27
- 5B + 12 = 27
- 5B = 27 - 12
- 5B = 15
- B = 15 / 5
- B = 3
Therefore, it takes Katrina 3 hours to make one bracelet and 4 hours to make one necklace.
