#### Transcript of Ratio and Proportion Examples 7-10

Ruben had a total of 56 apples and oranges. The ratio of the number of apples to oranges was 5 : 3. Later, he bought 34 more apples and oranges. After that the ratio of apples to oranges became 3 : 2. How many more apples did he buy?

Example 7

(cc) photo by theaucitron on Flickr

**Example 8**

Before

After

Apples : Oranges

Apples : Oranges

5 : 3

3 : 2

5

X 2

: 3

X 2

3

X 3

: 2

X 3

10 :

6

9 :

6

Total number of units

10 + 6 = 16 units

16 units

56 apples & oranges

1 unit

56 ÷ 16 = 3.5

10 units

3.5 X 10 =

35 apples

6 units

3.5 X 6 = 21 oranges

Before

After

Total number of units

9 + 6 = 15 units

15 units

56 + 34 = 90 apples & oranges

1 unit

90 ÷ 15 = 6

9 units

6 X 9 =

54 apples

Additional apples bought = 54 - 35

= 19 apples

Ruben bought 19 more apples.

There is an equal number of passes and failures in an exam. The ratio of boys to girls who passed is 5 : 3. The ratio of boys to girls who failed is 1 : 7. Find the ratio of boys who failed to boys who passed.

Pass

Fail

B : G

B : G

5 : 3

1 : 7

B

G

B

G

Total number of boys who failed

Total number of boys who passed

**=**

**1**

**5**

**X 1**

**X 1**

2

6

1

3

**=**

**1 X 1**

**5 X 3**

**=**

**1**

**15**

**The ratio of the total number of boys who failed**

to the total number of boys who passed is 1 : 15

**Example 8**

**Example 9**

If Tom gives May $12, he will have the same amount of money as May. If May gives Tom $12, the amount of money she has will be 1/7 that of Tom's. How much money does each of them have?

Tom

May

$12

$12

$12

$12

$12

If May gives Tom $12, she has 1/7 of what Tom has:

$12

Tom's $48

6

1 whole

Tom has $56 - $12 = $44

6

7

7

$48

= $56

Working

48

X

7

6

= 8 X 7

48

÷ 6

X

7

6

÷ 6

1

= 56

Amount of money May has = $44 - $24

Tom

$24

May

Tom has $44 and May has $20

= $20

**Example 10**

Joe bought some guppies, swordtails and goldfishes for $52.50. The ratio of the amount of money he spent on guppies, swordtails and goldfishes was 1 : 2 : 4. Each guppy cost 25 cents. The ratio of the number of swordtails to the number of guppies he bought was 2 : 3.

a.) Find the cost of a swordtail

b.) If each goldfish cost $1.25 more than a swordtail, how many goldfishes did he buy?

**Example 10**

**Example 10**

guppies : swordtails : goldfishes

1 : 2 : 4

1 + 2 + 4 = 7 units

7 units

$52.50

(guppies) 1 unit

52.50 ÷ 7 = $7.50

(swordtails) 2 units

(goldfishes) 4 units

7.50 X 2 = $15

7.50 X 4 = $30

1 guppy costs $0.25

Number of guppies bought = 7.50 ÷ 0.25

= 30 guppies

swordtails : guppies

2 : 3

3 units

30 guppies

1 unit

30 ÷ 3 = 10

2 units

10 X 2 = 20 swordtails

20 swordtails

$15

1 swordtail

15 ÷ 20 = $0.75

Each swordtail cost $0.75

Cost of each goldfish = $(1.25 + 0.75)

= $2

Total number of goldfishes he bought =

30 ÷ 2

= 15 goldfishes

Joe bought 15 goldfishes

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