First
Mrs Marie bought some apples. She use half of them and one more apple to make a pie. She then used half of the remainder and one more apple to make a pudding. She gave half of those that were left and one more apple to her children and had one apple left. How many apples did Mrs Marie buy at first?
(Use a Tree Branch Diagram)
(Working Backwards + Transfer and Complete) Method
(2nd Remainder)
1/2 of 2nd Remainder = 1 apple + 1 apple = 2 apples
2nd Remainder = 2 x 2 = 4 apples
(1st Remainder)
1/2 of 1st Remainder = 1 apple + Amount Left = 1 + 4 = 5 apples
1st Remainder = 5 x 2 = 10 apples
(Original)
1/2 of Original = 1 apple + Remainder = 1 + 10 = 11 apples
Original = 11 x 2 = 22 apples
Second
Jack was given an end-of-year bonus. First, he gave half of his bonus to his parents and $40 to his niece. Next, he donated 2/3 of the remaining bonus to a charity. Finally, he spent 1/3 of his remaining bonus on some clothes and $10 on a bag. If he had $110 left, how much was his bonus?
(2nd Remainder)
2/3 of 2nd Remainder = $10 + Left = $10 + $110 = $120
2nd Remainder = $180
(1st Remainder)
1/3 of 1st Remainder = $180
1st Remainder = $540
(Original)
1/2 of Original = $40 + 1st Remainder = $40 + $540= $580
Original = $1160
Third
Denise shared a sum of money with 3 other siblings, Andrew, Belle and Chris. She gave 1/3 of the money and an additional $30 to Andrew, then 1/4 of the remainder and an additional $3 to Belle and 1/3 of what was left and an additional $15 to Chris. Denise was left with $35. How much money did Denise have at first?
(2nd Remainder)
2/3 of 2nd Remainder = $15 + $35 = $50
2nd Remainder = $75
(1st Remainder)
3/4 of 1st Remainder = $3 + 2nd Remainder = $3 + $75 = $78
1st Remainder = $104
(Original)
2/3 of Original = $30 + 1st Remainder = $30 + $104 = $134
Original = $201
Fourth
Carol had a stack of name cards. She gave 1/3 of her cards and 30 more cards away in January. In February, she gave away 1/4 of the remainder and 45 more cards. In March, she gave away 1/5 of what was left and 20 more cards. Finally, she distributed all her remaining 40 cards in April. How many name cards did she have at first?
(2nd Remainder)
4/5 of 2nd Remainder = 20 cards + 40 cards = 60 cards
2nd Remainder = 75 cards
(1st Remainder)
3/4 of 1st Remainder = 45 cards + 2nd Remainder = 45 + 75 =120 cards
1st Remainder = 160 cards
(Original)
2/3 of Original = 30 cards + 1st Remainder = 30 + 160 = 190
Original = 285 cards
Fifth
Ali, Bala and Charles shared a tin of cookies. Ali took 5/6 of the tin of cookies and 1/3 of a cookie. Bala took 5/6 of the remaining cookies and 1/3 of a cookie. Charles received onIy 2 cookies. How many more cookies did Ali have than Bela?
Mrs Marie bought some apples. She use half of them and one more apple to make a pie. She then used half of the remainder and one more apple to make a pudding. She gave half of those that were left and one more apple to her children and had one apple left. How many apples did Mrs Marie buy at first?
(Use a Tree Branch Diagram)
(Working Backwards + Transfer and Complete) Method
(2nd Remainder)
1/2 of 2nd Remainder = 1 apple + 1 apple = 2 apples
2nd Remainder = 2 x 2 = 4 apples
(1st Remainder)
1/2 of 1st Remainder = 1 apple + Amount Left = 1 + 4 = 5 apples
1st Remainder = 5 x 2 = 10 apples
(Original)
1/2 of Original = 1 apple + Remainder = 1 + 10 = 11 apples
Original = 11 x 2 = 22 apples
Second
Jack was given an end-of-year bonus. First, he gave half of his bonus to his parents and $40 to his niece. Next, he donated 2/3 of the remaining bonus to a charity. Finally, he spent 1/3 of his remaining bonus on some clothes and $10 on a bag. If he had $110 left, how much was his bonus?
(2nd Remainder)
2/3 of 2nd Remainder = $10 + Left = $10 + $110 = $120
2nd Remainder = $180
(1st Remainder)
1/3 of 1st Remainder = $180
1st Remainder = $540
(Original)
1/2 of Original = $40 + 1st Remainder = $40 + $540= $580
Original = $1160
Third
Denise shared a sum of money with 3 other siblings, Andrew, Belle and Chris. She gave 1/3 of the money and an additional $30 to Andrew, then 1/4 of the remainder and an additional $3 to Belle and 1/3 of what was left and an additional $15 to Chris. Denise was left with $35. How much money did Denise have at first?
(2nd Remainder)
2/3 of 2nd Remainder = $15 + $35 = $50
2nd Remainder = $75
(1st Remainder)
3/4 of 1st Remainder = $3 + 2nd Remainder = $3 + $75 = $78
1st Remainder = $104
(Original)
2/3 of Original = $30 + 1st Remainder = $30 + $104 = $134
Original = $201
Fourth
Carol had a stack of name cards. She gave 1/3 of her cards and 30 more cards away in January. In February, she gave away 1/4 of the remainder and 45 more cards. In March, she gave away 1/5 of what was left and 20 more cards. Finally, she distributed all her remaining 40 cards in April. How many name cards did she have at first?
(2nd Remainder)
4/5 of 2nd Remainder = 20 cards + 40 cards = 60 cards
2nd Remainder = 75 cards
(1st Remainder)
3/4 of 1st Remainder = 45 cards + 2nd Remainder = 45 + 75 =120 cards
1st Remainder = 160 cards
(Original)
2/3 of Original = 30 cards + 1st Remainder = 30 + 160 = 190
Original = 285 cards
Fifth
Ali, Bala and Charles shared a tin of cookies. Ali took 5/6 of the tin of cookies and 1/3 of a cookie. Bala took 5/6 of the remaining cookies and 1/3 of a cookie. Charles received onIy 2 cookies. How many more cookies did Ali have than Bela?
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