rs and tables left ?

Question

Mr. PEREZ had 48 more chairs than tables in his furniture store. After selling off 5/6 of the chairs and 3/4 of the tables, there were 33 chairs and tables left.
A) How many tables were there at first?
B) What fraction of items sold were chairs ?

Answer 1

Let c = initial number of chairs

Let t = initial number of tables

 

c = t + 48      {equation 1}

 

c - (5/6)c + t - (3/4)t = 33

(1/6)c + (1/4)t = 33

Multiply through by 12 to clear fractions

2c + 3t = 396      {equation 2}

 

Since we already have defined c in terms of t in equation 1,

replace c with t+48 in equation 2 and solve for t

 

2(t+48) + 3t = 396

2t + 96 + 3t = 396

5t = 300

t = 60

 

There were initially 60 tables and 108 chairs

 

Items sold:  (5/6)c = (5/6)(108) = 90 chairs

                  (3/4)t = (3/4)60 = 45 tables

                  Total items sold:   135

 

Chairs sold as a fraction:  90/135 = 2/3

Answer 2

C = T + 48 ---> T = C-48

 

1/6C + 1/4T = 33 <---- 5/6 of the chairs sold, so 1/6 remains; 3/4 of the tables sold, so 1/4 remains

 

1/6C + (1/4)(C-48) = 33

 

(1/6)C + (1/4)C - 12 = 33

 

(5/12)C - 12 = 33

 

(5/12)C = 45

 

C = 45 * 12/5 = 9*12  = 108

 

108 Chairs, 108-48 = 60 tables.

 

5/6 of the chairs, or 90 of them, sold. So 18 remain.

3/4 of the tables, or 45 of them, sold. so 15 remain.

That total is 33.

The answers are correct.