# PSLE Math Challenging “Double If” question

Today, I will like to share with you a method that doesn’t require complicated algebra to solve a PSLE Math Challenging “Double If” question.

Example: A farmer has some chickens and ducks. If he sells 2 chickens and 3 ducks every day, there will be 50 chickens left when all the ducks have been sold. If he sells 3 chickens and 2 ducks every day, there will be 25 chickens left when all the ducks have been sold.

a) how many ducks are there?

b) how many chickens are there ?

Solutions:

List down the 2 cases.

Case 1: 2 Chickens and 3 ducks per day, 50 chickens left

Case 2: 3 chickens and 2 ducks per day, 25 chickens left

Write down the selling ratio for both cases

Case 1

Chicken : Duck = 2u : 3u

Case 2

Chicken : Duck = 3u : 2u

Notice that in both cases, the ducks are sold out. So I need to make the ratio of ducks in both cases the same.

Case 1 (Times 2 to both sides)

Chicken : Duck = 2u : 3u = 4u : 6u

Case 2 (Times 3 to both sides)

Chicken : Duck = 3u : 2u = 9u : 6u

The initial number of chickens in both cases are the same. So,

4u + 50 = 9u + 25

5u = 25

1u = 5

Answer for a) The total number of ducks is 5 * 6 = 30 ducks

Answer for b) To find the number of chickens, we can use either case 1 or 2.

If we use case 1, number of chickens = 5 * 4 + 50 = 70 chickens

Check your answer!

Let’s use case 2 to check our answer. If there are 30 ducks, number of days to sell the ducks = 30 / 2 = 15

Number of chickens sold = 15 * 3 = 45

Leftover chickens = 70 – 45 = 25 chickens (Correct!)

Now it’s your turn to try!

1) Vicky and Jane were given a certain amount of money to spend. If Vicky spent $90 and Jane spent $30, Vicky would have $100 left when Jane had spent all her money. If Vicky spent $30 and Jane spent $90, Vicky would have $580 left when Jane had spent all her money.

a) Find the total amount of money given to Jane. (Ans: $180)

b) Find the total amount of money given to Vicky. (Ans: $640)

2) Tammy and Sharon have some money. If Tammy spent $60 each day and Sharon spent $30 each day, Tammy is left with $400 when Sharon spent all her money. If Sharon spent $60 each day and Tammy spent $30 each day, Tammy is left with $1150 when Sharon spent all her money. How much money do the two girls have altogether? (Ans: $1900)

3) Alicia and Bruce are given some money each. If Alicia spends three times as much as Bruce, She will have $1000 more when Bruce has spent all his money. If Alicia spends half of what Bruce spends, she will have $2200 when Bruce has spent all his money. What is the total sum of money given to Alicia and Bruce? (Ans: $2920)

4) Jack and Jill owned a chicken farm each. If Jack and Jill sold 60 chickens and 30 chickens respectively in a day, Jack would have 300 chickens left when Jill has sold all her chickens. If Jack sold 30 chickens a day and Jill sold 60 chickens a day, Jack would have 930 chickens left when Jill has sold all her chickens. Find the number of chickens Jack has on his farm. (Ans: 1140)

**Contact Us!**

Math is one of the few subjects that you can easily train/practise till you score an **A**. At Intellicat Tuition School, we teach you how to break down complicated problem sums into easy, solvable steps. Feel free to contact us at **enquiry@gradesolution.com.sg** or call us at **6280 6841.**

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By Jimmy Ling

Director, Math Tutor

Intellicat Tuition School

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