Question

A cafe sells puffs. 5/9 are beef and 1/3 are chicken. The remaining 18 are tuna. Calculate 1. What fraction of the puffs are tuna and 2. How many puffs are there in all. I really need to see the working for this.

Answer 1

5/9 + 1/3 + tuna = 1

tuna =   1  - 5/9 - 1/3.           LCM = 9

tuna = 9/9 - 5/9 - 3/9 = (9 - 5 - 3)/9 = 1/9

Fraction of tuna = 1/9

Let all the puffs be x.   Recall there are 18 tuna

(1/9)x = 18

x/9 = 18

x = 9*18

x = 162

There are 162 puffs in all.

Answer 2

Let n be the total number of puffs. Now we can write:
$n=\frac{5}{9}n+\frac{1}{3}n+18$
Adding the fractional value of n, we get:
$n=\frac{5+3}{9}n+18$
Simplifying and rearranging gives us:
$n-\frac{8}{9}n=18$
Therefore we can simplify to get:
$\frac{1}{9}n=18$
and finally
$n=18\times9=?$
The fraction of the puff that are tuna is found from:
$\frac{18}{18\times9}=\frac{1}{9}$