Question

Bonnie and Jenna are trading books. If
Bonnie were to give three of her books to Jenna, Jenna would have four times as many books as Bonnie. But if Jenna were to give five of her books to Bonnie instead, Bonnie would then have one fewer book than Jenna
had before they traded. How many books does Bonnie have to begin with?​

Answer 1

Answer:

7 books

Step-by-step explanation:

Let Bonnie begin with ‘x’ number of books.

Let Jenna begin with ‘y’ number of books.

Case (i): Bonnie gives three books to Jenna.

Number of books Bonnie has = x - 3

Number of books Jenna has = y + 3

Given that;

Jenna would have 4 times as many books as Bonnie

y + 3 = 4(x - 3)

y + 3 = 4x - 12

4x - y = 15 ……. Eq (1)

Case (ii): Jenna gives 5 books to Bonnie.

Number of books Bonnie has = x + 5

Number of books Jenna has = y - 4

Given that;

Bonnie would have 1 fewer book than Jenna before they traded.

Number of books Jenna had before they traded = y

So,

x + 5 = y - 1

x - y = -6 ……….. Eq (2)

Solving equations (1) & (2)

    4x - y = 15

    x - y   = -6

 (-)  (+)     (+)

———————-

   3x      = 21

     x = 7

Therefore, Bonnie has to begin with x = 7 books.