A woodworking shop makes tables and chairs.
To make a chair, 8 min is needed on the lathe and 8 min is needed on the sander. To make a table, 8 min is needed on the lathe and 20 min us needed on the sander.
The lathe operator works 6h/day, and the sander operator works 7h/day. How many chairs and tables can they make in one day working at this capacity?
lathe: 8 min/chair, 8 min/table, 6 hours/day
sander: 8 min/chair, 20 min/table, 7 hours/day
let c be the number of chairs made in a day, and t be the number of tables made in one day
8 min/chair *c chairs +8 min/table *t tables = 6 hrs *60 min/hr *1 day/day <=== from the lathe use
8 min/chair *c chairs +20 min/table *t tables = 7 hrs *60 min/hr *1 day/day <=== from the sander use
simplify and subtract equations
…. (8c +8t = 360)
– …(8c +20t = 420)
……0 …-12t = -60
t = 5
back substitute for c
8c = 360 -8t
c = 45 -5 = 40
so they can make 5 tables and 40 chairs in one day in this manner