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?

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:

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:

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

From equation (1) we will get,

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

Therefore, Giselle worked 18 hours as blacksmith.

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

Therefore, Giselle worked 12 hours as carpenter.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

answer: -1

step-by-step explanation: