Given: Equal Ratio 1 : 1 (Before) + Proportional Ratio (Change)
First
Raymond and Wilson had an equal amount of money. Raymond spent $20 each day and Wilson spent $30 each day. When Wilson had spent all his money, Raymond still had $120 left. How much did each of them have at the beginning?
Raymond and Wilson had an equal amount of money. Raymond spent $20 each day and Wilson spent $30 each day. When Wilson had spent all his money, Raymond still had $120 left. How much did each of them have at the beginning?
Second
The number of strawberry sweets was the same as the number of mint sweets. Andy packed the sweets into several identical boxes. He packed 2 strawberry sweets and 5 mint sweets into each box. When the last mint sweet was packed, there were still 21 strawberry sweets left. How many mint sweets were there at the beginning?
The number of strawberry sweets was the same as the number of mint sweets. Andy packed the sweets into several identical boxes. He packed 2 strawberry sweets and 5 mint sweets into each box. When the last mint sweet was packed, there were still 21 strawberry sweets left. How many mint sweets were there at the beginning?
Third
In a sales promotion, a supermarket was giving 3 packets of orange juice free for every 7 packets of guava juice bought by the customer. There was an equal number of orange juice packets and guava juice packets at first. When the supermarket had finished selling all the guava juice there were 48 packets of orange juice left. How many packets of orange juice were there at first?
In a sales promotion, a supermarket was giving 3 packets of orange juice free for every 7 packets of guava juice bought by the customer. There was an equal number of orange juice packets and guava juice packets at first. When the supermarket had finished selling all the guava juice there were 48 packets of orange juice left. How many packets of orange juice were there at first?
Fourth
A fruit seller packed each of his apples together with his pears and was left with no remainder. Later, he changed his mind and decided to pack his 4 apples with 9 pears. When he had finished packing all his pears, he was left with 75 apples. How many apples did he have in the beginning?
A fruit seller packed each of his apples together with his pears and was left with no remainder. Later, he changed his mind and decided to pack his 4 apples with 9 pears. When he had finished packing all his pears, he was left with 75 apples. How many apples did he have in the beginning?
Given: Non-Equal Ratio (Before) + Proportional Ratio (Change)
First
There were some exercise books and files in a box. The number of exercise books was twice the number of files. Each time, 7 exercise books and 5 files were taken out from the box, After a whiIe, only 30 exercise books were left. How many files were taken out?
There were some exercise books and files in a box. The number of exercise books was twice the number of files. Each time, 7 exercise books and 5 files were taken out from the box, After a whiIe, only 30 exercise books were left. How many files were taken out?
Second
Jar A contained mint candies and Jar B contained chocolate candies. The number of mint candles was 1 1/2 times the number of chocolate candies. 4 mint candles and 6 chocolate candies were distributed to each child in a class until only 25 mint candies were left. How many chocolate candies were there in Jar B at first?
Jar A contained mint candies and Jar B contained chocolate candies. The number of mint candles was 1 1/2 times the number of chocolate candies. 4 mint candles and 6 chocolate candies were distributed to each child in a class until only 25 mint candies were left. How many chocolate candies were there in Jar B at first?
Third
In a hobby shop, the number of Roman soldier figurines was 3/5 fewer than the number of Greek soldier figurines. Ralph and Dan were asked to paint the figurines. In every hour, they managed to paint 1 Roman soldier figurine and 10 Greek soldier figurines. After some time, they were left with 75 Roman soldier figurines to paint. How many Roman and Greek soldier figurines were there altogether at first?
In a hobby shop, the number of Roman soldier figurines was 3/5 fewer than the number of Greek soldier figurines. Ralph and Dan were asked to paint the figurines. In every hour, they managed to paint 1 Roman soldier figurine and 10 Greek soldier figurines. After some time, they were left with 75 Roman soldier figurines to paint. How many Roman and Greek soldier figurines were there altogether at first?
Fourth
In a party, the volume of syrup in a bottle is 40% of the volume of water in another bottle. 10 ml of syrup and 200 ml of water were used each time to make a cup of juice. After a certain number of cups of juice were prepared, it was found that only 280 ml of syrup was left and no water was left. How much water was there at first?
Given: 2 Proportional Ratios (Case 1 & 2)
First
In a party, the volume of syrup in a bottle is 40% of the volume of water in another bottle. 10 ml of syrup and 200 ml of water were used each time to make a cup of juice. After a certain number of cups of juice were prepared, it was found that only 280 ml of syrup was left and no water was left. How much water was there at first?
Given: 2 Proportional Ratios (Case 1 & 2)
First
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?
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?
(Case I)
Chicken : Duck
= 2 : 3
= 4 : 6
Chicken : Duck
= 2 : 3
= 4 : 6
(Case II)
Chicken : Duck
= 3 : 2
= 9 : 6
Chicken : Duck
= 3 : 2
= 9 : 6
9u + 25 left = 4u + 50 left
9u - 4u = 50 - 25
5u = 25
Ducks = 6u = 25 ÷ 5 × 6 = 30
Chickens = 4u + 50
= 25 ÷ 5 × 4 + 50 = 70
9u - 4u = 50 - 25
5u = 25
Ducks = 6u = 25 ÷ 5 × 6 = 30
Chickens = 4u + 50
= 25 ÷ 5 × 4 + 50 = 70
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