Answer:
Giselle worked 18 hours as blacksmith and 12 hours as carpenter.
Step-by-step explanation:
Let C be the number of hours Giselle works as carpenter and B represent the number of hours Giselle works as blacksmith.
We have been given that last week, Giselle worked both jobs for a total of 30 hours. We can represent this information in an equation as:
![B+C=30...(1)](https://tex.z-dn.net/?f=B%2BC%3D30...%281%29)
We are also told that she earns $25 per hour as a blacksmith, so so amount earned in B hours will be 25B.
As Giselle earns $20 per hour as a carpenter, so amount earned in C hours will be 20C.
Since she earned a total of $690 last week by doing both jobs, we can represent this information in an equation as:
![25B+20C=690...(2)](https://tex.z-dn.net/?f=25B%2B20C%3D690...%282%29)
We will use substitution method to solve our system of linear equations.
From equation (1) we will get,
![C=30-B](https://tex.z-dn.net/?f=C%3D30-B)
Substituting this value in equation (2) we will get,
![25B+20(30-B)=690](https://tex.z-dn.net/?f=25B%2B20%2830-B%29%3D690)
![25B+600-20B=690](https://tex.z-dn.net/?f=25B%2B600-20B%3D690)
![25B+600-600-20B=690-600](https://tex.z-dn.net/?f=25B%2B600-600-20B%3D690-600)
![25B-20B=690-600](https://tex.z-dn.net/?f=25B-20B%3D690-600)
![5B=90](https://tex.z-dn.net/?f=5B%3D90)
![\frac{5B}{5}=\frac{90}](https://tex.z-dn.net/?f=%5Cfrac%7B5B%7D%7B5%7D%3D%5Cfrac%7B90%7D)
![B=18](https://tex.z-dn.net/?f=B%3D18)
Therefore, Giselle worked 18 hours as blacksmith.
Upon substituting B=18 in equation (1) we will get,
![18+C=30](https://tex.z-dn.net/?f=18%2BC%3D30)
![18-18+C=30-18](https://tex.z-dn.net/?f=18-18%2BC%3D30-18)
![C=12](https://tex.z-dn.net/?f=C%3D12)
Therefore, Giselle worked 12 hours as carpenter.