Question

A worker on the production line is paid a base salary of ​$230.00 per week plus ​$0.78 for each unit produced. Write an equation to represent her earnings of ​$446.84 for a week when she produced x units. How many units did she ​produce? Use pencil and paper. If the worker had produced twice that number of​ units, what would his earnings have​ been? Here is what it should look like, 446.84=230+.78x

How Many Units did they make

Answer 1

(a)

We are given

A worker on the production line is paid a base salary of ​$230.00 per week

so, base salary =230

Let's assume number pencils produced as x

plus ​$0.78 for each unit produced

now, we can find equation for earnings

`E(x)=230+0.78x`

now, we are given

her earnings of ​$446.84 for a week when she produced x units

so, we can set E(x)=446.84

and then we can solve for x

`446.84=230+0.78x`

`230\cdot \:100+0.78x\cdot \:100=446.84\cdot \:100`

`23000+78x=44684`

`23000+78x-23000=44684-23000`

`78x=21684`

`(78x)/(78)=(21684)/(78)`

`x=278`

so, number of pencils = 278........Answer

(b)

If the worker had produced twice that number of​ units

so, number of pencils =2*278=556

now, we can find earnings

`E(x)=230+0.78x`

now, we can plug x=556

`E(556)=230+0.78*556`

`E(556)=663.68`.................Answer