The merchant gets 15 ingots for every 2 spice bags. To find the total for 12 bags, divide 12 by 2 to get 6 pairs, then multiply 6 by 15, resulting in 90 copper ingots.
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The square root spiral starts with a base triangle of sides 1 and 1, giving a hypotenuse of root 2. Each successive triangle adds a side of 1, yielding hypotenuses of root 2, root 3, root 4, and continuing sequentially.
Squaring x + y + z = 0 gives x2 + y2 + z2 + 2(xy + yz + zx) = 0. Since xy + yz + zx = 0, it simplifies to x2 + y2 + z2 = 0. ...
First, find a common denominator for 1/6 and 2/5, which is 30, giving 5/30 and 12/30. The five rational numbers lying between them are 6/30, 7/30, 8/30, 9/30, and 10/30.
To find 6 rational numbers between 3 and 4, convert them into fractions with a denominator of 7, giving 21/7 and 28/7. The intermediate numbers are 22/7, 23/7, 24/7, 25/7, 26/7, and 27/7.