Chapter 2. Using model diagrams to solve problems involving total

Problem 1

Ben has 6 boxes. Ben and William have 17 boxes altogether. How many boxes does William have?

Solution

Draw a box to represent the 6 boxes Ben has and a bigger box to represent the number of boxes William has.

Number of balls William has = 17 - 6 = 11

Problem 2

Ben and William have 19 boxes altogether. William has 5 boxes more than Ben. How many boxes does William have?

Solution

Draw a box to represent the number of boxes Ben has and a bigger box to represent the number of boxes William has.

2 units = 19 - 5 = 14

1 unit = 14 ÷ 2 = 7

Number of boxes William has

= 1 unit + 5

= 7 + 5

= 12

Problem 3

William has twice as many apples as Ben. They have 24 apples. How many apples does William have?

Solution

3 units = 24

1 unit = 24 ÷ 3 = 8

Number of boxes William has

= 2 units

= 2 x 8

= 16

Problem 4

William has 2 times more apples than Ben. They have 24 apples altogether. How many apples does William have?

Solution

4 units = 24

1 unit = 24 ÷ 4 = 6

Number of boxes William has

= 3 units

= 3 x 6

= 18

Worksheet 2

1. Jim has 5 apples. Jim and Jenny have 14 apples together. How many apples does Jenny have?

3. Jim has three times more apples than Jenny. They have 35 apples together. How many apples does Jim have?