Question

Giselle works as a carpenter and as a

blacksmith.
She earns $20 per hour as a carpenter and
$25 per hour as a blacksmith. Last week,
Giselle worked both jobs for a total of 30
hours, and earned a total of $690.
How long did Giselle work as a
carpenter last week, and how long did
she work as a blacksmith?
Giselle worked as a carpenter for
hours and as a blacksmith for
hours last week.

Answer 1

12 hours as a carpenter and 18 as a blacksmith.

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