N11 Numbers: Word Problems using Models

COMMON TERMS in WORD PROBLEM / PROBLEM SUM

Using Model for WORD PROBLEM

Example:

There are 3 times more apples than oranges. There are 8 apples. How many oranges are there?

Understanding the sentence:

The word ‘3 times’ is used to describe apples.

The term ‘more’ can be expressed as:

                               4u = 8

                                u=8/4 = 2.  There are 2 oranges.

Model Method(Storytelling - Who What How)

(1) Read the sentence carefully and spot the word patterns.

(2) Note (a) Who are there and the number/fractions in the sentence. 

(3) Note what happened, link to model form, and answer the question.

Method: 

Step 1:  Who and their Number(Underline)

Step 2:  What is the story? (Draw and link)

Step 3: How to Solve (Answer/Conclusion)

Example 1 (More Less)

There are thrice as many apples as banana. There are 12 fruits. How many apples are there?

Step 1:  Who + Number  (Underline)

             Who           number             

Apple                                    (3/1)

Banana        

  Total            12

 Step 2:  What is the story? Draw and link.

Step 3: How to Solve (Answer/Conclusion)

              There are 12 fruits

             3u + u = 12 

                   4u = 12

                     u = 3.  

             There are 3x3 = 9 apples

Example 2 (Come and Go)

John had 12 more pies than Clive at first. After John had eaten 4 pies, he had twice as many pies as Clive in the end. How many pies did Clive have?
Method

Example 3 (Come and Go)

Janice had 32 more sweets than Rebecca as first. After Rebecca had eaten 14 of his sweets, Janice had thrice as many sweets as Rebecca. How many sweets did Janice have at first?

Example 4 (Come and Go, changed multiples)

There were twice as many men as women at a party. After 15 women had left the party, the number of men in the party was thrice the number of the remaining women. How many adults attended this party?

Method (Come and Go)

Example 5 (Growing Up)

Kevin is 8 years old. His father is 34 years old. In how many years' time will his father's age three times of Kevin's age?

Method

In 5 year times, father's age will be three times of Kevin's age.

Example
Dennis had 120 marbles more than Jean at first. After Dennis had given away 150 of his marbles to Calvin, Jean had thrice as many marbles as Dennis. Find the number of marbles Dennis had at first.

(Using Model)

Step1: Circle/Underline Keywords. Actors?          Dennis, Jean 

Step2:  Numbers? Draw and Link

                                            

Step3: Solve: 

                                       J         D

                                   u = 3(u – 30)

                                   u = 3u - 90

                                 2u = 90, u = 45

Dennis has 45 + 120 = 165 marbles at first

Example

Tammy had $800 more than Kris at first. After Kris had spent $340, Tammy had 5 times as much money as Kris. Find the amount of money Tammy had at first.

(Using Model)

Step1: Circle/Underline Keywords. Actors?          Tammy, Kris   

                                             

Step2:  Numbers? Draw and Link

     

Step3: Solve: 

                              T                        K

                         u + 800   =     5(u-340)

                         u + 800 = 5u - 1700

                                 4u = 2500

                                   u = 625

     Tammy has $625 + $800 = $1425

Example3

(Using Model)

Joshua had 45 more stickers than Melvin at first. After Melvin used 15 of his stickers, Joshua had thrice as many stickers as Melvin in the end. Find number of stickers Joshua had at first.

Step1: Circle/Underline Keywords. Actors?          Joshua, Melvin   

                                             

Step2:  Numbers? Draw and Link

         

Step3: Solve: 

   Link - Joshua has thrice as many sweets as Melvin

                                          J             M

           ->      u + 45 = 3(u-15)

                                  u + 45 = 3u - 45

                                  2u = 90

                                    u = 45

Joshua has 45 + 45 = 90 stickers at first

Practice – Solve using Algebra method

 ~~~~ END ~~~~ :)