If 4x + 5y = 140 and 4x / 5y = 2 / 5, then find y - x.

Question: If 4x + 5y = 140 and 4x / 5y = 2 / 5, then find y - x.

Solution:
We are given:
⇒ 4x / 5y = 2 / 5

We simplify:
x / y = (5 / 4) × (2 / 5)
⇒ x / y = 2 / 4 = 1 / 2
∴ x = y / 2

Also given:
4x + 5y = 140

Substitute x = y / 2:
⇒ 4 × (y / 2) + 5y = 140
⇒ (4y / 2) + 5y = 140
⇒ (2y + 5y) = 140
⇒ 7y = 140
⇒ y = 20

Then x = y / 2 = 10
So, 20 - 10 = 10