Answer:
Option E: 24.
Step-by-step explanation:
When Caleb (C) has 20 more books than Danica (D), we have:
[tex] C = 20 + D [/tex] (1)
Now, when Caleb gives Danica half of his books:
[tex] C' = C - \frac{C}{2} [/tex] (2)
Danica will have 4 more books than Caleb, so:
[tex] D' = D + \frac{C}{2} [/tex] (3)
Also we have that:
[tex] D' = C' + 4 [/tex] (4)
By entering equation (2) and equation (3) into equation (4) we have:
[tex] D + \frac{C}{2} = C - \frac{C}{2} + 4 [/tex] (5)
From (1) we have:
[tex] D = C - 20 [/tex] (6)
By entering (6) into (5):
[tex] C - 20 + \frac{C}{2} = C - \frac{C}{2} + 4 [/tex]
[tex] C = 24 [/tex]
And, from (6):
[tex] D = C - 20 = 24 - 20 = 4 [/tex]
Therefore, the correct option is E, Caleb had to start with 24 books.
I hope it helps you!
