How many items were in Jo's grocery bag?

Question

Help please, and could you show all the steps?

 

Chen bought a bag of groceries weighing 15 pounds. His friend, Jo, bought a bag of groceries that also weighed 15 pounds, but contained one less item. The average weighted per item for Jo's groceries was a 1/2 pound more than for Chen's. How many items were in Jo's grocery bag?

Answer 1

let x=# of Chen's items

let x-1=# of Jo's items

ley y=# of pounds each of Chen's items weigh

let y+0.5=# of pounds each of Jo's items weigh

each bag weighs 15 pounds

xy=15

(x-1)(y+0.5)=15

from xy=15 we have y=15/x

substituting we get...

(x-1)[(15/x)+0.5]=15

multiply both sides by x

(x-1)(15+0.5x)=15x

15x-15+0.5x^2-0.5x=15x

subtract 15x from both sides

-15+0.5x^2-0.5x=0

multiply both sides by 2

-30+x^2-x=0

x^2-x-30=0

factor

(x-6)(x+5)=0

x-6=0

x=6

Chen has 6 items weighing 15 pounds

Jo has 6-1=5 items weighing 15 pounds

check:15/6=2.5 pounds for each of Chen's items

          15/5=3 pounds for each of Jo's items

                3 is 0.5 pounds more than 2.5 pounds