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# Advanced Math/Amount - Solution/ Explanation

Question
Here is a problem with solution. I don't understand parts of the solution:

In a quantity of metal, the brass is 10 pounds more than 2/3 of the total, the iron 4 1/2 pounds less than 1/6 of the total, and nickel 2 pounds less than 1/7 of the brass. Calculate amount of metal.

Let x = total

2x/3 + 10 = brass

x/6 - 4 1/2 = iron

2x/21 + 10/7 - 2 = nickel *

2x/3 + x/6 + 2x/21 + 10/7 + 3 1/2 = x *

4x + x + 4x/7 + 60/7 + 21 = 6x

4x/7 + 60/7 + 21 = x

4x + 60 + 21 * 7 = 7x

60 + 21 * 7 = 3x

20 + 7 * 7 = x

69 = x

* I don't understand what the 2x/21 or 3 1/2 is. Thanks.

The 2x/21 comes from applying the distributive rule.
n = (1/7)b - 2
= (1/7)(2x/3 + 10) - 2
= (1/7)2x/3 + (1/7)10 - 2
= 2x/21 + 10/7 - 2

The 3½ comes from 10-4½-2:
x = b + i + n
= (2x/3 + 10) + (x/6 - 4½) + (2x/21 + 10/7 - 2)
= (2x/3 + x/6 + 2x/21) + (10 - 4½ + 10/7 - 2)
= (2x/3 + x/6 + 2x/21) + (10/7 + 10-4½-2)
= 2x/3 + x/6 + 2x/21 + 10/7 + 3½
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