Let's call those numbers "a"(the smaller number) and "b"(the bigger number).
The question is telling us two equations. The ratio is 4:10
a/b = 4/10
And the sum of the two numbers is 380.
a + b = 380
Combining those two equations we have a solvable system.
From the first equation, we get
a/b = 4/10
Multiplying both sides by "b"
a = (4/10) x b
plugging this "a" into the second equation we get:
(4/10) x b + b = 380
[(4/10) + 1] x b = 380
(14/10) x b = 380
Then
b = (10/14) x 380
Calculating the result, we get the bigger number
b = 271
making another substitution on the second equation, now with our new result, we get
a + 271 = 380
a = 109