Question

There were 120 tables and chairs in a furniture shop. 4/9 of the tables and 5/7 of the chairs were made of wood. The rest of the 44 tables and chairs were made of metal. How many tables were made of wood?

Answer 1

tables --- t
chairs ---- c

t + c = 120 or c = 120-t

made of wood: (4/9)t + (5/7)c
made of metal: (5/9)t + 2/7)c = 44
times 63 , the LCD
35t + 18c = 2772
sub in c = 120-t
35t + 18(120-t) = 2772
35t + 2160 - 18t = 2772
17t = 612
t = 36
then c = 120-36 = 84

tables made of wood = (4/9)t = (4/9)(36) = 16

check:
wooden tables = (4/9)(36) = 16
wooden chairs = (5/7)(84) = 60
metal tables = (5/9)(36) = 20
metal chairs = (2/7)(84) = 24
total = 120
all checks out