Answer:
12 hours as a carpenter and 18 as a blacksmith.
Step-by-step explanation:
So she earns 20$ per hour as a carpenter. c can represent the amount of hours she worked as a carpenter, and the coefficient will be 20 (salary)
So she earns 25$ per hour as a blacksmith, b can represent the amount of hours she worked as a blacksmith, and 25 will be the coefficient (salary)
So we have the two equations:
c + b = 30
20c + 25b = 690
Now we can solve for c in terms of b and substitute that into the second equation:
Original equation:
c + b = 30
Subtract b from both sides
c = -b + 30
Original equation:
20c + 25b = 690
Substitute -b + 30 as c
20(-b + 30) + 25b = 690
Distribute the 20
-20b + 600 + 25b = 690
Simplify the equation
600 + 5b = 690
Subtract 600 from both sides
5b = 90
Divide both sides by 5
b = 18
Now plug this into either of the original equations to solve for c, but the first equation b + c = 30 is the easiest, so I'll use that equation
Original equation
b + c = 30
Substitute 18 as b
18 + c = 30
Subtract 18 from both sides
12 = c
- given;
- given;
- as vertical angles (by vertical angles theorem)