 # Question

In the beginning Alex Bill Carl and Dan had 63 marbles.Then Alex lost 3 marbles. Bill’s aunt bought another 3 marbles for Bill. Carl’s mother rewarded Carl by doubling what he had originally. Dan lost half of what he had. In the end the 4 children had equal number of marbles.

1. How many more marbles had Alex than Bill at first
2. How many marbles had alex at first

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(a)

3 + 3 = 6

(b)

63/9 = 7
7 x 2 + 3 = 17 (Alex)

Ans : (a) 6 marbles; (b) 17 marbles.

Pl. exp the steps for a and b

By model drawing method,

At first —
Alex : 1u + 1u + 3 = 2u + 3
Bill : 1u + 1u – 3 + 2u – 3
Carl : 1u
Dan : 1u + 1u = 2u

Then —
Alex : 2u + 3 – 3 = 2u
Bill : 2u – 3 + 3 = 2u
Carl : 1u x 2 = 2u
Dan : 4u/2 = 2u

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A model presentation would probably explain well but I have problem uploading images.

At first        In the end

A         2u + 9           2u + 6

B         2u + 3            2u + 6

C          1u + 3           2u + 6

D          4u + 12         2u + 6

Total    9u + 27

9u + 27 = 63

9u = 27

1u = 4

a) A more than B at first = 9-3 =6

b) A at first = 2u + 9

= 8+9

=17