During the spring you do yard cleanup for households and you also paint houses you earn $8 an hour cleaning up and $12 an hour painting last summer you worked a total of 400 hours and earned $3800 how many hours did you spend during your cleanup and how many hours did you spend painting

you spent 250 hours during your cleanup.

you spent 150 hours painting

Step-by-step explanation:

Let x represent the number of hours that you spent during your cleanup.

Let y represent the number of hours that you spent painting.

you earn $8 an hour cleaning up and $12 an hour painting last summer and you earned $3800 . it means that

8x + 12y = 3800- - - - - - - - - -- 1

You worked a total of 400 hours. This means that

x + y = 400

Substituting x = 400 - y into equation 1, it becomes

8(400 - y) + 12y = 3800

3200 - 8y + 12y = 3800

- 8y + 12y = 3800 - 3200

4y = 600

y = 600/4 = 150 hours

Substituting y = 150 into x = 400 - y, it becomes

x = 400 - 150

x = 250 hours

boxplot

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!