Many difficult problems can be solved with the "make a supposition" method. It is a very powerful, easy-to-use method. It is very useful for problems where you need to solve for two unknown quantities.
– Total is given, Difference is given.
– Total is given, Average is given.
– Two scenarios are given.
1. Suppose a fixed quantity of 1 item. (Can set it to 0, or to max quantity)
2. Check, what is the difference.
3. Suppose the quantity of that item changes by 1.
4. Check, what is the difference.
5. Calculate how much the difference changes when the quantity changes by 1.
6. Calculate how much the quantity needs to change by.
To see when it can be used, try to see if you can fix a quantity of one item and calculate the resulting quantity of the other item. Usually this involves a "total".
I’ll share a few more examples soon!
Here’re more examples
Learn to recognise these type of questions:
There are 85 plates of fried noodles for 80 people. Each adult eats 2 plates of fried noodles and every 3 children share 1 plate of fried noodles. How many adults and how many children are there? (35 adults and 45 children)
A total of 360 teachers and pupils participated in tree planting. Each teacher planted 3 trees and each group of 3 pupils planted 2 trees. If 520 trees were planted altogether, how many pupils were there? (240)
There were 54 cars and bicycles in a car park. Someone removed 1 wheel each from 4 bicycles. As a result, there were 180 wheels left. How many cars were there?(38)
A courier company charged $25 for every large parcel and $15 for every small parcel delivered safely. However, a penalty of $50 was charged for every damaged parcel regardless of size. This month, the company delivered 120 parcels of which 1/4 of them were small parcels. It collected a total of $2000 after paying a penalty for an equal numbers of large and small parcels.How many large parcels were delivered safely?
20 boys and girls sold tickets for a funfair. Each ticket was sold at $5.Each boy sold 5 tickets and each girl sold 3 tickets. The amount collected by the boys was $20 more than the amount collected by the girls. Find a) how many girls were there in the group b) how many tickets were sold altogether? (8 boys, 12 girls, 76 tickets)
A class of 40 pupils helped to carry bundles of old newspapers in an event organised to collect funds for the old folks. Each boy carried 3 stacks of newspapers and each girl carried 2 stacks. Altogether, the boys carried 30 more stacks than the girls. What is the ratio of the number of boys to the number of girls in the class?(11:9)
In a Maths quiz, each pupil had to answer 20 questions. 5 points were given for each correct answer and 2 points were taken away from each wrong answer. Mirabel answered all questions and scored 79 points. How many questions did she answer correctly? (17)
There are some goats, chickens and cows in a farm. There are 3 times many chickens as cows. John finds out that among the animals, there are a total of 32 heads and 92 legs. How many goats are there? (18,6 ,8 )
I have 38 coins and they are made up of 50-cent and 20-cent coins. Their total value is $13.60. What is the ratio of the number of 20-cent coins to the number of 50-cent coins? (9:10)
A group of 24 children sold some tickets for a charity show. Each ticket was sold at $5. Each boy sold 5 tickets and each girl sold 3 tickets. The boys collected $40 more than the girls. (a) How many girls were there in the group? (14) (b) How many tickets were sold altogether? (92)
After the tsunami, 250 blankets were given out to the people .Three children shared 1 blanket while 2 adults shared 1 blanket. If there were 650 people, how many of them were adults.(650)
Mrs B used either 4 red buttons or 2 blue buttons to make each dress. The total number of dresses she made was 35. The total number of red buttons used was 74 more than the total number of red buttons used. (a) how many red buttons were used altogether?(96) (b) how many blue buttons were used altogether?(22)
Kumaran had 64 coins in his coin box. There were 20-cent coins and 50-cent coins. The total value of all the coins was $18.50. How many 20-cent coins and how many 50-cent coins were there?(45,19)
At a Science competition, 25 problems were given. Each correct answer earned 4 points, and 2 points were deducted for each incorrect answer. Liang Hong answered all but one of the problems receiving a score of 66. How many correct answers did she have?(19)
Mr Lau sells notebooks at $2 each and files at $3 each. After he sold 100 notebooks and files, the amount he collected from the sale of notebooks was $60 more than than the amount collected from the sale of files. How many notebooks did Mr Lau sell?(72)
Brandon had 30 spelling tests and collected 36 games cards. With every full marks he scored for a spelling test, he received 2 games cards from his teacher. When he did not score full marks, he had to return 1 games card. a) how many spelling tests did brandon score full marks?(22) b) if Brandon wanted to receive a total of 51 games cards, how many spelling tests could he afford not to score full marks?(3)
A spider has 8 legs while a beetle has 6 legs. James caught 24 spiders and beetles altogether. He found that the number of spiders’ legs were 66 more than the number of beetles’ legs. How many spiders and beetles did he catch? (9 beetles, 15 spiders)
Mr Lum has 38 pieces of copper wire and aluminium wire. The total length of all the copper wires is 15.3m longer than the total length of all the aluminium wires. Each piece of copper wire is 1.7m long while each piece of aluminium wire is 1.2m long. How many pieces of aluminium wire does Mr Lum have? (17)
A bill of $83 was paid with $10, $5 and $1 notes. If 15 notes were used, how many notes of each kind were used? (4 $10, 8 $5, 3 $1)