# Linear Problem – Grade 10?

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?

• Anonymous
6 days ago

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