Joseph owner of Lanza Electronics and Home Applicances,is preparing to open a second store in Los Angeles,California.Joseph pays the manger of his original Orange County store a weekly base pay of...

Joseph owner of Lanza Electronics and Home Applicances,is preparing to open a second store in Los Angeles,California.Joseph pays the manger of his original Orange County store a weekly base pay of $700 plus 25% of the store 's total weekly sales.The marking indicates that with a good sales force in the  new store L.A store,the total weekly sales will be same as the Organe Country store.To motivate sales at the new store.Joseph will pay the manger a smaller base of $400 and a higher commission rate 35%.He predicts that both mangers will have the same total sales and earn the same weekly pay with this salarly plan.Determine the amount weekly sales and the manger's weekly salary at each store with this plan.

Asked on by kim609

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lemjay | High School Teacher | (Level 3) Senior Educator

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Let x be the weekly sales of each store.

Then, set-up the equation for the weekly salary of the two managers.

At Orange County store, the manager weekly base pay is $700 plus 25% of x. So, his weekly salary can be represented by:

`S_1=700+0.25x`

And at the L.A. store, the weekly base of the manager is $400 plus 35% of x. Hence, his weekly salary is:

`S_2=400+0.35x`

Now that the equations of the salary of both managers are known, set S1 and S2 equal to each other to determine the weekly sales of each store that results to same weekly pay.

`S_1=S_2`

`700+0.25x=400+0.35x`

From here, bring together the terms with x on one side of the equation.

`700+0.25x-0.25x=400+0.35x-0.25x`

`700=400+0.10x`

Also, bring together the terms without x on the other side of the equation.

`700-400=400-400+0.10x`

`300=0.10x`

Then, divide both sides by 0.10 to get x only at one side of the equation.

`300/0.10=(0.10x)/0.10`

`3000=x`

Hence, the weekly sales of each store in order for the two mangers to have same weekly salary should be 3000.

Next, solve for the weekly salary. To do so, substitute the value of x to either S1 or S2 equation.

`S_1=700+0.25x=700+0.25(3000)=700+750`

`S_1=1450`

Thus, the weekly salary of the managers in each store is $1450.

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