Question

Lucy and Zachary work at a furniture store. Lucy is paid $200 per week plus 7.5% of her total sales in dollars, x x, which can be represented by g ( x ) = 200 + 0.075 x g(x)=200+0.075x. Zachary is paid $233 per week plus 6% of his total sales in dollars, x x, which can be represented by f ( x ) = 233 + 0.06 x f(x)=233+0.06x. Determine the value of x x, in dollars, that will make their weekly pay the same.

Answer 1

`f(x) = g(x)`

`200 +0.075 x= 233 +0.06 x`

We can subtract from both sides 0.06x and we got:

`0.075 x-0.06x +200 = 233`

And now we can subtract 200 from both sides we got:

`0.015 x = 33`

And dividing both sides by 0.015 we got:

`x = (33)/(0.015)= 2200`

And then the final anwer would be x =2200

Explanation:

For this case we have the following function for the total sales of Lucy is given by:

`g(x) = 200 +0.075 x`

And the function for the total sales of Zachary is given by:

`f(x) =233 +0.06 x`

And we want to determine the value of x, in dollars, that will make their weekly pay the same, so we can set equal the two functions:

`f(x) = g(x)`

`200 +0.075 x= 233 +0.06 x`

We can subtract from both sides 0.06x and we got:

`0.075 x-0.06x +200 = 233`

And now we can subtract 200 from both sides we got:

`0.015 x = 33`

And dividing both sides by 0.015 we got:

`x = (33)/(0.015)= 2200`

And then the final anwer would be x =2200