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

Answer:

Option E: 24.

Step-by-step 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:

$C' = C - \frac{C}{2}$   (2)

Danica will have 4 more books than Caleb, so:

$D' = D + \frac{C}{2}$     (3)    

Also we have that:

$D' = C' + 4$   (4)  

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

$D + \frac{C}{2} = C - \frac{C}{2} + 4$   (5)

From (1) we have:

$D = C - 20$   (6)

By entering (6) into (5):

$C - 20 + \frac{C}{2} = C - \frac{C}{2} + 4$

$C = 24$

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!