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 ?
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
Chicken : Duck = 2u : 3u
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)
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 firstname.lastname@example.org or call us at 6280 6841.
Intellicat Tuition School is located at 1030A Upper Serangoon Road S(534767).
By Jimmy Ling
Director, Math Tutor
Intellicat Tuition School
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