A question I got Stuck on!

Question

A glass is 1/3 full. Then 75cm3 of orange juice is poured in.
The glass is now 3/4 full. What is the total volume of the glass?

A glass is $\frac{1}{3}$ full. Then 75cm3 of orange juice is poured in. 
The glass is now $\frac{3}{4}$ full. What is the total volume of the glass?

Answer 1

V=total volume

(1/3)V+75=(3/4)V

75=(3/4)V-(1/3)V

75=(9/12)V-(4/12)V

75=(5/12)V

multiply both sides by 12/5

(12/5)(5/12)V=(12/5)(75)

V=12*15)  (after simplifying)

V=180 cm³ is the total volume

check: (1/3)(180)=60

60+75=135

135/180=27/36=3/4

Answer 2

3/4 - 1/3 = 9/12 - 4/12 = 5/12

 

The 75cm³ is 5/12 of the total volume.

 

(5/12)v = 75

(12/5)(5/12)v = 75(12/5)

v = 180

 

The total volume is 180 cm³.