Let

x = Daniel's age

y = Lucy's age

Daniel’s age is 7 more than three times his daughter Lucy’s age means:

x = 7 + 3y

The difference between twice Daniel’s age and five times Lucy’s age is 24 means:

2x - 5y = 24

We have the following system of equations:

x = 7 + 3y

2x - 5y = 24

........

click here to see the system of equations solved for x and y

........

x = 37 years

y = 10 years

Daniel is 37 years old while his daughter, Lucy, is 10 years old.