Q:

Annette, Barb, and Carlita work in a clothing shop. One day the three had combined sales of $1480. Annette sold $120 more than Barb. Barb and Carlita combined sold $280 more than Annette. Write and solve a linear system to find out how much did each person sold.

Accepted Solution

A:
Answer:The quantity sold by Annette was $600The quantity sold by Barb was $480The quantity sold by Carlita was $400Step-by-step explanation:Letx ----> quantity sold by Annettey ---> quantity sold by Barbz ---> quantity sold by Carlitawe know that[tex]x+y+z=1,480[/tex] ----> equation A[tex]x=y+120[/tex] ----> equation B[tex]y+z=x+280[/tex] ----> equation Csubstitute equation C in equation A and solve for x[tex]x+(x+280)=1,480[/tex] [tex]2x=1,480-280[/tex] [tex]2x=1,200[/tex] [tex]x=\$600[/tex] Find the value of y[tex]x=y+120[/tex] [tex]600=y+120[/tex] [tex]y=600-120=\$480[/tex] Find the value of z[tex]x+y+z=1,480[/tex][tex]600+480+z=1,480[/tex][tex]1,080+z=1,480[/tex][tex]z=\$400[/tex]thereforeThe quantity sold by Annette was $600The quantity sold by Barb was $480The quantity sold by Carlita was $400