Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Two workers in a holiday boutique are filling stockings with small gifts and candy. Katie has already filled 3 stockings and will continue to fill them at a rate of 1 stocking per hour. Peter, who just arrived to help, can fill 4 stockings per hour. At some point, Peter will catch up with Katie and they will have completed the same number of stockings. How long will that take? How many stockings will each worker have filled by then?In ____ hours, the workers will each have filled _____ stockings.

Answer 1

Two workers in a holiday boutique are filling stockings with small gifts and candy.

Katie has already filled 3 stockings and will continue to fill them at a rate of 1 stocking per hour.

3 + x

Peter, who just arrived to help, can fill 4 stockings per hour.

4 x

At some point, Peter will catch up with Katie and they will have completed the same number of stockings.

3 + x = 4x

3 = 4x -x

3 x =3

x = 3/3

x =1 hour How long will that take?

How many stockings will each worker have filled by then?

Katie = 3 + 1 = 4

Peter = 4 x 1 = 4