Question

Caleb has 20 more books than Danica. If Caleb gives Danica half of his books, Danica will have 4 more books than Caleb. How many books did Caleb have to start with? E. 24 F. 34 G. 44 H. 55

Answer 1

Option E: 24.

Explanation:

When Caleb (C) has 20 more books than Danica (D), we have:

`C = 20 + D` (1)

Now, when Caleb gives Danica half of his books:

`C' = C - (C)/(2)` (2)

Danica will have 4 more books than Caleb, so:

`D' = D + (C)/(2)` (3)

Also we have that:

`D' = C' + 4` (4)

By entering equation (2) and equation (3) into equation (4) we have:

`D + (C)/(2) = C - (C)/(2) + 4` (5)

From (1) we have:

`D = C - 20` (6)

By entering (6) into (5):

`C - 20 + (C)/(2) = C - (C)/(2) + 4`

`C = 24`

And, from (6):

`D = C - 20 = 24 - 20 = 4`

Therefore, the correct option is E, Caleb had to start with 24 books.

I hope it helps you!