The total number of coins Balu had in his collection was <u>216 coins</u>, computed using the linear equation in one variable, <u>x = x/2 + x/3 + 36</u>.
Asian coins were 1/2 a fraction of this, that is, (1/2)*216 = <u>108 coins</u>.
We assume the total coins with Balu to be x.
The fraction of coins from Asian countries = 1/2.
Thus, the number of coins from the Asian countries = 1/2 of x = x/2.
The fraction of coins from European countries = 1/3.
Thus, the number of coins from the European countries = 1/3 of x = x/3.
The number of coins from America = 36.
Thus, the total number of coins = x/2 + x/3 + 36.
But, we assumed that the total number of coins is x.
Thus, we get a linear equation in one variable as follows:
x = x/2 + x/3 + 36.
We solve this equation as follows:
x = x/2 + x/3 + 36,
or, x - x/2 - x/3 = 36,
or, (6x - 3x - 2x)/6 = 36,
or, x/6 = 36,
or, x = 36*6 = 216.
Thus, the total number of coins Balu had in his collection was <u>216 coins</u>, computed using the linear equation in one variable, <u>x = x/2 + x/3 + 36</u>.
Asian coins were 1/2 a fraction of this, that is, (1/2)*216 = <u>108 coins</u>.
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