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We might have started with this:

          TABLES      CHAIRS
START          T      45 + T

But we soon realize that we need to compute 25% of T (i.e. 1/4 of T)
and 5/9 of (45 + T). We can use fractions but it tends to be messy.
Since 4 x 9 = 36, let us use T = 36u instead. It makes life easier
because 1/4 x 36u = 9u and 5/9 of (45 + 36u) = 25 + 20u. So

          TABLES       CHAIRS
START        36u     45 + 36u
SOLD          9u     25 + 20u

Since 91 more chairs were sold, so 25 + 20u = 91 + 9u.
This can be solved to get 11u = 66 so u = 6.

Number of tables left unsold is 36u - 9u = 27u = 27 x 6 = 162.

CHECK:
         TABLES   CHAIRS
START       216      261
SOLD         54      145   (145 - 54 = 91, 145/261 = 5/9)
UNSOLD      162

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0 Replies 1 Like ✔Accepted Answer

Let me try the stupid way 🙂

Let there be T tables.
So there are T + 45 chairs.

(5/9)(T + 45) – (25/100)T = 91
(5/9)T + 25 – (1/4)T = 91
((20-9)/36)T = 91 – 25
(11/36)T = 66
T = (36/11)66 = 216

The number of tables left unsold is 3/4 T = (3/4) 216 = 162 #

You are right.  It is a mouthful 😛 

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