Set 1 (Before) vs Set 2 (After)
Amount (2 Changes)
First
Amount (2 Changes)
First
Felicia collected 1/5 as many seashells as Gareth at the beach at first. Then, Felicia found 5 more seashells and Gareth found 12 more seashells. The ratio of the number of seashells Gareth had to the number of seashells Felicia had became 4 : 1. How many seashells did Gareth have at first?
(Before)
Felicia : Gareth
= 1u : 5u
(Change)
Felicia >> +5
Gareth >> +12
Felicia : Gareth
= 1u : 5u
(Change)
Felicia >> +5
Gareth >> +12
(After)
Felicia : Gareth
= 1p : 4p
Felicia : Gareth
= 1p : 4p
Approach 1:
Equalise and Eliminate the Parts
Equalise and Eliminate the Parts
(Felicia)
1u + 5 = 1p
4u + 20 = 4p
1u + 5 = 1p
4u + 20 = 4p
(Gareth)
5u + 12 = 4p
5u + 12 = 4p
1u - 8 = 0
1u = 8
1u = 8
Gareth (Before) = 5u = 40
Approach 2:
Equalise and Eliminate the Units
Equalise and Eliminate the Units
(Felicia)
1u + 5 = 1p
5u + 25 = 5p
1u + 5 = 1p
5u + 25 = 5p
(Gareth)
5u + 12 = 4p
5u + 12 = 4p
13 = 1p
5p = 65
5p = 65
Gareth (Before) = 5p - 25 = 65 - 25 = 40
Second
Second
Jane had 2/5 as many kiwi fruits as Bernice at first. Jane bought another 8 kiwi fruits and Bernice ate 5 kiwi fruits. Then, Jane had 4/5 as many kiwi fruits as Bernice. Find the number of kiwi fruits Jane had at first.
(Before)
Jane : Bernice
= 2u : 5u
(Change)
Jane >> +8
Bernice >> -5
Jane : Bernice
= 2u : 5u
(Change)
Jane >> +8
Bernice >> -5
(After)
Jane : Bernice
= 4p : 5p
Jane : Bernice
= 4p : 5p
Approach 1:
Equalise and Eliminate Parts
Equalise and Eliminate Parts
(Jane)
2u + 8 = 4p
10u + 40 = 20p
2u + 8 = 4p
10u + 40 = 20p
(Bernice)
5u - 5 = 5p
20u - 20 = 20p
5u - 5 = 5p
20u - 20 = 20p
10u - 20 - 40 = 0
10u - 60 = 0
10u = 60
10u - 60 = 0
10u = 60
Jane (Before) = 2u = 12
Approach 2:
Equalise and Eliminate the Units
Equalise and Eliminate the Units
(Jane)
2u + 8 = 4p
10u + 40 = 20p
2u + 8 = 4p
10u + 40 = 20p
(Bernice)
5u - 5 = 5p
10u - 10 = 10p
5u - 5 = 5p
10u - 10 = 10p
40 - (-10) = 10p
10p = 50
4p = 20
10p = 50
4p = 20
Jane (Before) = 2u = 4p - 8 = 20 - 8 = 12
Third
At a pet shop, the number of puppies was 1/2 of the number of kittens at first. After 80 kittens and 12 puppies were sold, the number of kittens left was 2/5 of the number of puppies left. What was the total number of puppies and kittens in the pet shop at first?
Fourth
The number of spoons and forks in a restaurant was 3 : 7 respectively. After the chef bought 6 more spoons and 4 more forks, the number of spoons became 1/2 of the number of forks. How many forks did the chef have after the purchase?
Fifth
At a pet shop, the number of puppies was 1/2 of the number of kittens at first. After 80 kittens and 12 puppies were sold, the number of kittens left was 2/5 of the number of puppies left. What was the total number of puppies and kittens in the pet shop at first?
Fourth
The number of spoons and forks in a restaurant was 3 : 7 respectively. After the chef bought 6 more spoons and 4 more forks, the number of spoons became 1/2 of the number of forks. How many forks did the chef have after the purchase?
Fifth
The ratio of the number of boys to the number of girls on a club last year was 2 : 3. This year, 44 boys joined the club and 12 girls left. The ratio of the number of boys to the number of girls becomes 5 : 1. How many members are there in the club this year?
Sixth
Rosa had 0.75 of the amount Clement had. When he spent $372 and she spent $124, she would have twice as much as the amount he had left. How much did each person have at first?
3u - 124 = 2p
4u - 372 = 1p
8u - 744 = 2p
5u - 744 + 124 = 0
5u = 620
1u = 124
3u = 373
4u = 496
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