Final answer:
Firstly, the full value of the number was found by dividing 80 by 2/5, resulting in 200. Then, 3/4 of this number was calculated to be 150.
Step-by-step explanation:
To solve this problem, let us first determine the full value of the number when 2/5 of it is 80. We can write a simple equation for this:
(2/5) × number = 80
Now, solve for the 'number' by multiplying both sides by the reciprocal of 2/5, which is 5/2.
number = 80 × (5/2)
number = 200
Now that we have the full value of the number, let's find 3/4 of this number.
(3/4) × 200 = 150
So, 3/4 of the same number is 150.