Chapter 3. Using model diagrams to solve problems involving one party giving to another

Chapter 3. Using model diagrams to solve problems involving one party giving to another

Problem 1

Adam and Zach had the same number of books. Pete then gave Zach 9 books. Zach now has 4 times more books than Adam. How many books does Adam have?

Solution

Draw two boxes equal in size to represent that Adam and Zach have the same number of books.

After Pete gives 9 books to Zach, Zach has 4 times more books than Adam.

3 units = 9

1 unit = 9 ÷ 3 = 3

Number of books Zach has

= 4 units

= 4 x 3

= 12 books

Problem 2

Adam had two times as many books as Zach. After Adam gave 20 books to Peter, Zach now has 3 times as many books as Adam. How many books does Adam have at first?

Solution

At first, Adam had two times as many books as Zach

After Adam gave 20 books to Peter, Zach now has 3 times as many books as Adam

Cut Adam’s boxes into units of the same size.

5 units = 20

1 unit = 20 ÷ 5 = 4

Number of books Adam had at first = 6 units = 6 x 4 = 24 books

Worksheet 3

1. Jim and Jenny have the same number of apples. After Jim gives Adam 18 apples, Jenny has 4 times as many apples as Jim. How many marbles does Jenny have?

2. Jeremy has twice as many sweets as Jack. After Jeremy gives Adam 21 sweets, Jack now has twice as many sweets as Jack. How many sweets does Jack have?

3. Jill has twice as much money as Joseph. After she spends $15, Joseph now has three times as much money as she. How much money did Joseph have?

4. Jasper have some cats and 50 dogs. After he sells away 18 dogs, he has four times as many dogs as cats. How many cats did he have?

5. Albert have some apples and oranges. He has 15 more apples than oranges. After he gave away 21 apples, he has three times as many oranges as apples. How many oranges does Albert have?