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steposvetlana [31]

3 years ago

8

Fred and George had some savings in the ratio 3 : 4 respectively.  They decided to buy a birthday present for their little siste

r sharing the cost at ratio 2 : 3 respectively.  After they have bought the present, Fred has already spent half of his money. George only has £21 left over.  Find the price of the present.

1 answer:

ollegr [7]3 years ago

3 0

The price of the present is £45.

<u>Step-by-step explanation</u>:

<u>step 1</u> :

Let,

Savings of Fred = 3x

Savings of George = 4x

<u>step 2</u> :

share of Fred = 2y

share of George = 3y

∴ Total cost of the gift = 2y + 3y = 5y

<u>step 3</u> :

According to the question given,

Fred has already spent half of his money = 3x - 2y = (1/2)3x

George only has £21 left over = 4x - 3y = 21

<u>step 4</u> :

solve for x in the first equation,

3x - (3/2)x = 2y

6x - 3x = 4y

3x = 4y

x = (4/3)y

<u>step 5</u> :

substitute x=(4/3)y in the second equation to find y,

4x - 3y = 21

4(4/3)y - 3y = 21

(16/3)y - 3y = 21

16y - 9y = 63

7y = 63

y = 9

<u>step 6</u> :

The total cost of the gift = 2y + 3y

Price of the present = 5y = 5 $\times$ 9 = 45

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b) We need a sample size of at least 4145.

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$0.02\sqrt{n} = 2.575\sqrt{0.5*0.5}$

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