Answer: Total fish are 27, difference is 18
Step-by-step explanation:
Given: one-third of the fish in Liam's fish tank were added today. Half of the other fish were a gift to Liam last week. the other 9 came from Liam's old fish tank.
To Find: Number of the fish in the tank, difference between the number of fish Liam had in his old tank and the number he has now.
Solution: Let the total fish in tank be = x
total fish added today = [tex]\frac{1}{3}\times \text{x}[/tex]
Total fish left = [tex]\text{x}-\frac{1}{3}\text{x}[/tex]= [tex]\frac{2}{3}\text{x}[/tex]
Fish gifted to him last week = [tex]\frac{1}{2}\times\frac{2}{3}\times \text{x}[/tex]
= [tex]\frac{1}{3}\text{x}[/tex]
Fish left = [tex]\frac{2}{3}\text{x}[/tex] - [tex]\frac{1}{3}\text{x}[/tex]
[tex]\frac{1}{3}\text{x}[/tex]
now,
fish left in the tank are =[tex]\frac{1}{3}\text{x}[/tex]
fish from liam's old tank = 9 = fish left in the tank
[tex]\frac{1}{3}\text{x}[/tex] = 9
[tex]\text{x}[/tex]=[tex]27[/tex]
Total fish in liam's new tank= [tex]27[/tex]
difference between the number of fish Liam had in his old tank and the number he has now
= [tex]27-9=18[/tex]
Total Fish in Liam's new tank are 27 and difference between the number of fish Liam had in his old tank and the number he has now is 18.