SOLUTION: Lucas has 18 coins 5c, 10c,20c in his pocket. There are three times as many 10c coins as 20c coins. the number of each type of coins is divisible by 3,and the number of 10c coins i

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Question 1115578: Lucas has 18 coins 5c, 10c,20c in his pocket. There are three times as many 10c coins as 20c coins. the number of each type of coins is divisible by 3,and the number of 10c coins is also divisible by 2. how many of each type coins does Lucas have?
Answer by Fombitz(32388) About Me  (Show Source):
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X-number of 5c coins
Y-number of 10c coins
Z-number of 20c coins
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"18 coins"
X%2BY%2BZ=18
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"three times as many 10c coins as 20c coins"
Y=3Z
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X%2B3Z%2BZ=18
X%2B4Z=18
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Since X is divisible by 2 and 3, it is a multiple of 6 and the smallest value it can be is 6.
Since Y and Z are also divisible by 3, the smallest values they can have are 3.
Start with X=6,
6%2B4Z=18
4Z=12
Z=3
So then,
Y=3%283%29
Y=9
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(6,9,3) is a solution.
If you try X=12,
12%2B4Z=18
4Z=6
Not an integer solution.
So there is only one solution.