# Question

Ahmad and Ali had a total of 360 buttons. Ahmad gave 1/5 of his buttons to Ali. Ali then gave 1/4 of his buttons to Ahmad. In the end, each of them had the same number of buttons. How many buttons did Nadia have at first?

2 Answers

# Answer

Ahmad and Ali had a total of 360 buttons. Ahmad gave 1/5 of his buttons to Ali. Ali then gave 1/4 of his buttons to Ahmad. In the end, each of them had the same number of buttons. How many buttons did each boy have at first?

360/2 = 180
3/4 ——- 180
4/4 ——- 240 (buttons Ali had before he gave 1/4 of his buttons to Ahmad)
360 – 240 = 120 (buttons Ahmad had after he gave 1/5 of his buttons to Ali)
4/5 ——- 120
5/5 ——- 150 (buttons Ahmad had at first)
360 – 150 = 210 (buttons Ali Had at first)

Ans : Ahmad — 150 buttons; Ali — 210 buttons.

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Ahmad     Ali           Total

In the end        180            180          360

3u=180

1u=60

Ahmad rtn       120            240         360

1u to Ali

4u=120

1u=30

Ali rtn 1u

to Ahmad         150            210          360

Ahmad at first = 150 buttons

Ali at first = 210 buttons

(Is there a typo error in the question because there is no Nadia in the earlier part of the question?)

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