Ratio P5

The ratio of the amount of money Jenny had to the amount of money Siti had was 3:4. The next day, their parent gave each of them some money. Siti received twice as much as Jenny. The ratio then became 5:8. If both girls had a total of $70 at first, how much did Siti receive?
J    [][][] [][]
S [][][][] [][][][]

7 u --> $70
4 u --> 4/7 x 70 = $40

Siti received $40.

Ratio P5

1. There were some flowers at a flower shop. The ratio of the number of roses to the number of tulips was 2:3. When 50 more roses and 30 more tulips were added, the ratio of the number of roses to the number of tulips became 5:6. How many flowers were there at first?

  R          T              6R           5T

-----------------------------------------

  2    :     3             12      :     15

+50       +30          +300         +150

-----------------------------------------

  5    :     6             30      :     30

-----------------------------------------

12 u + 300 --> 15 u + 150

3 u --> 300 – 150 = 150

1 u --> 150 ÷ 3 = 50

5 u --> 5 x 50 = 250 flowers

There were 250 flowers at first.

Alternative method

R        [  4 u ]<   50   >          2 : 3 = 4 : 6. Instead of                

T        [   6 u     ]<  30   >      using 2 and 4 units, use

                                                        4 and 6 units (because of 6 p)

----------------------------------

          [1 u][5]    x    5

R         [        5 p       ] 

T         [          6 p          ]

          [1 u][5]      x       6     Make use of T (before) to

                                          construct T (after)

5 u + 25 --> 4 u + 50          Compare R

1 u --> 50 – 25 = 25

10 u --> 10 x 25 = 250 flowers

There were 250 flowers at first.

Ratio P5

5. A box contained 50cent coins and 20cent coins in the ratio 2:3. When I took out four 50cent coins, exchanged them for 20cent coins, and then put the money back into the box, the ratio became 2:7. Find the sum of money in the box.

4 x 50 = 200

200 ÷ 20 = 10

  50¢      20¢    3 x 50¢   2 x 20¢

---------------------------------------

  2    :      3         6     :     6

- 4       + 10      - 12       + 20

---------------------------------------

  2    :      7         6     :    14

---------------------------------------

6 u + 12 --> 14 u – 20

8 u --> 12 + 20 = 32

1 u --> 32 ÷ 8 = 4

2 x 4 = 8

8 x 0.50 = $4

7 x 4 = 28

28 x 0.20 = $5.60

4 + 5.60 = $9.60

The sum of money in the box was $9.60.

Ratio P5 A002

A bag of cookies was distributed to 3 girls, Amber, Christine and Doris. Amber received 45 cookies and the remaining cookies were distributed to Christine and Doris in the ratio 2 : 5. If Christine received 1/5 of the total cookies, how many cookies were there in the bag at first.

The remaining cookies were distributed to Christine and Doris in the ratio 2 : 5. Christine received 1/5 of the total cookies.

2 -- 1/5

Express the number of cookies Doris and Amber had in fractions.

5 -- 5/2 x 1/5 = 5/10

5/2 x 1/5 = 5/10

10/10 – 1/5 x 2/2 – 5/10 = 3/10  

Amber received 45 cookies.

3 u --> 45

10 u --> 10/3 x 45 = 150 cookies

There were 150 cookies in the bag at first.

Ratio P5 2009 SA1 P2 MGS Q18

18. Elsie had $320 less than Grace. Elsie gave Grace $170. Now the ratio of Elsie’s money to Grace’s money is 3 : 5. How much money did Elsie have at first?

E  [        ][        ][        ][170]

G  [        ][        ][        ][        ][        ]

     [        ][        ][        ][170][320][170]

2 u -- > 170 + 320 + 170 = 660

1 u -- > 660 ÷ 2 = 330

3 u -- > 3 x 330 = 990

990 + 170 = $1160

Elsie had $1160 at first.

Ratio P5 A001

Ali and Muthu share a sum of money. If Ali gives 1/2 of his share to Muthu, Muthu will have $48 more than Ali. If Ali gives 1/4 of his share to Muthu, Muthu will have $28 more than Ali. What is the ratio of Ali's share to Muthu's share?

Firstly given 1/2 and 1/4, make each unit the same. [1/2 x 2/2 = 2/4, denominator the same as 1/4 –-> Total 4 units for A.]

If Ali gives 1/2 of his share to Muthu, Muthu will have $48 more than Ali.
Then, draw A – 4 units with 2 units shaded and M – 2 units + $48.

A   [][][][]

M   [][][  48   ]

From above model, you can derive that originally M has $48.

If Ali gives 1/4 of his share to Muthu, Muthu will have $28 more than Ali.

Next draw A - 4 units with 1 unit shaded and M - 1 unit + $48. Then redraw M - 3 units + $28.

A   [][][][]

M   [][  48   ]

    [][][][ 28 ]

Compare M, you will get 2 units --> 48 – 28. [Difference of $48 and $28]

2 u -- > 48 – 28 = 20

1 u -- > 20 ÷ 2 = 10

A : 4 u -- > 10 x 4 = 40

M -- > 48

A : M = 40 : 48 = 5 : 6

The ratio of Ali's share to Muthu's share is 5 : 6.


Alternative method

Firstly given 1/2 and 1/4, make each unit the same. [1/2 x 2/2 = 2/4, denominator the same as 1/4 –-> Total 4 units for A.]

If Ali gives 1/2 (=2/4) of his share to Muthu, Muthu will have $48 more than Ali.

Ali will be left with 2 units, Muthu will have 2 units + $48. [Total is 4 units + $48]

If Ali gives 1/4 of his share to Muthu, Muthu will have $28 more than Ali.

Ali will be left with 3 units, Muthu will have 3 units + $28. . [Total is 6 units + $28]

As above involve units from Ali to Muthu, the Total remains a Constant [Constant Total].

6 u + 28 -- > 4 u + 48

2 u --> 48 – 28 = 20

1u --> 20 ÷ 2 = 10

A : 4 u --> 10 x 4 = 40

M --> 48

A : M = 40 : 48 = 5 : 6

The ratio of Ali's share to Muthu's share is 5 : 6.