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=(5)/(9)n+(1)/(3)n+18`
Adding the fractional value of n, we get:

`n=(5+3)/(9)n+18`
Simplifying and rearranging gives us:

`n-(8)/(9)n=18`
Therefore we can simplify to get:

`(1)/(9)n=18`
and finally

`n=18*9=?`
The fraction of the puff that are tuna is found from:

`(18)/(18*9)=(1)/(9)`