Answer:
lesser number: 9
greater number:41
Explanation:
Given: a+b=50
Use the word problem to create equation: 5a-4=b
We can solve for either variables, we'll solve for b(greater number) first:
a=50-b
Plug a into other equation:
5(50-b)-4=b
250-5b-4=b
246-5b=b
246=6b
b=41
Plug what we found for b into equation to solve for a(lesser number):
a+41=50
a=9
Verify:
5(9)-4=41 ?
45-4=41
41=41 Checks out.
Hope this helps.