Question

Giselle works as a carpenter and as a blacksmith. She earns \$20$20 per hour as a carpenter and \$25$25 per hour as a blacksmith. Last week, Giselle worked both jobs for a total of 3030 hours, and earned a total of \$690$690. How long did Giselle work as a carpenter last week, and how long did she work as a blacksmith?

Answer 1

Giselle worked 18 hours as blacksmith and 12 hours as carpenter.

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)`

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)`

We will use substitution method to solve our system of linear equations.

From equation (1) we will get,

`C=30-B`

Substituting this value in equation (2) we will get,

`25B+20(30-B)=690`

`25B+600-20B=690`

`25B+600-600-20B=690-600`

`25B-20B=690-600`

`5B=90`

`(5B)/(5)=\frac{90}`

`B=18`

Therefore, Giselle worked 18 hours as blacksmith.

Upon substituting B=18 in equation (1) we will get,

`18+C=30`

`18-18+C=30-18`

`C=12`

Therefore, Giselle worked 12 hours as carpenter.