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Twice a number increased by 11 is equal to 32 less than three times the number. Find out the number.
Let x = the number. Now translate every part of the sentence. Twice a number increased through 11 is 2x + 11; 32 less than 3 times a number is 3x - 32. Set the expressions equal to each other: 2x + 11 = 3x - 32. Subtract 2x from both sides of the equation: 2x - 2x + 11 = 3x - 2x - 32. Simplify: 11 = x - 32. Add 32 to both sides of the equation: 11 + 32 = x - 32 + 32. The variable is now alone: x = 43.
Catalans Conjecture
1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
11-b=34
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