Question

Arthur, Yusuf, and Bill had some stamps in the ratio 3: 5: 6. When Yusuf gave some stamps to Arthur and Bill gave Arthur 42 stamps more than what Yusuf gave Arthur, they all had the same number of stamps each. How many stamps did Yusuf have at first?

Answer 1

210 stamps

Explanation:

Given:

• Arthur ⇒ a = 3 k
• Yusuf ⇒ y = 5k
• Bill ⇒ b = 6k

Yusuf gave x stamps to Arthur, then:

• y = 5k -x
• a = 3k + x

Bill gave Arthur 42 stamps more than Yusuf gave to Arthur, then:

• b = 6k - (x+42)
• a = 3k + x + x + 42

Now all 3 have same amount of stamps:

• 5k -x = 6k - x - 42 = 3k + 2x + 42

From the first part of the equation we get:

• 6k - 5k = 42 + x - x
• k = 42

How many stamps did Yusuf have at first?

• y = 5k
• y =5*42
• y = 210 stamps

Yusuf had 210 stamps at first