answer:Let's denote the ages of a, b, and c as A, B, and C respectively. From the information given, we have: 1. A = B + 2 (since a is two years older than b) 2. B = some times as old as C (we need to find this multiplier) 3. A + B + C = 27 (the total of their ages) 4. B = 10 (since b is 10 years old) Now, let's substitute the values we know into the equations: From equation 1: A = 10 + 2 A = 12 Now we have A's age and B's age, we can find C's age using equation 3: 12 (A's age) + 10 (B's age) + C = 27 22 + C = 27 C = 27 - 22 C = 5 Now we have B's age and C's age, we can find the ratio of B's age to C's age: B : C = 10 : 5 To simplify the ratio, we divide both sides by the greatest common divisor of B and C, which is 5: B : C = (10/5) : (5/5) B : C = 2 : 1 So the ratio of B's age to C's age is boxed{2:1} .

answer:First, identify the perfect squares around 50 to find the integer part of its square root: - sqrt{49} = 7 and sqrt{64} = 8, hence 7 < sqrt{50} < 8. - The largest integer less than sqrt{50} is 7. Next, square the integer: - 7^2 = 49. Thus, lfloorsqrt{50}rfloor^2 = boxed{49}.

answer:Since in the arithmetic sequence {a_n}, a_4 + a_8 = 16, then a_4 + a_8 = 2a_6 = 16, solving this gives a_6 = 8, thus a_2 + a_6 + a_10 = 3a_6 = 24. Therefore, the correct choice is: D. Using the general formula of an arithmetic sequence, we get a_6 = 8, and a_2 + a_6 + a_10 = 3a_6, which allows us to find the result. This question tests the method of finding the sum of three terms in an arithmetic sequence, which is a basic problem. When solving it, one should carefully read the problem and properly apply the properties of arithmetic sequences. boxed{text{D}}

answer:1. **Option A**: [ frac{2x+y}{y} = frac{2x}{y} + frac{y}{y} = 2cdotfrac{5}{6} + 1 = frac{10}{6} + frac{6}{6} = frac{16}{6} ] Hence, frac{2x+y{y} = frac{16}{6}} is correct. 2. **Option B**: [ frac{y}{y-2x} = left(frac{y-2x}{y}right)^{-1} = left(frac{y}{y} - frac{2x}{y}right)^{-1} = left(1 - 2cdotfrac{5}{6}right)^{-1} = left(1 - frac{10}{6}right)^{-1} = left(frac{6}{6} - frac{10}{6}right)^{-1} = left(-frac{4}{6}right)^{-1} = frac{6}{-4} ] Thus, frac{y{y-2x} = frac{6}{-4}} holds true. 3. **Option C**: [ frac{3x+3y}{x} = frac{3x}{x} + frac{3y}{x} = 3 + 3cdotfrac{5}{6} = 3 + frac{15}{6} = 3 + frac{5}{2} = frac{6}{2} + frac{5}{2} = frac{11}{2} ] Thus, frac{3x+3y{x} = frac{11}{2}} does not match frac{18}{5}, showing Option C is incorrect. 4. **Option D**: [ frac{x}{3y} = frac{1}{3}cdotfrac{x}{y} = frac{1}{3}cdotfrac{5}{6} = frac{5}{18} ] Thus, frac{x{3y} = frac{5}{18}} matches. 5. **Option E**: [ frac{x-2y}{y} = frac{x}{y} - frac{2y}{y} = frac{5}{6} - 2 = frac{5}{6} - frac{12}{6} = -frac{7}{6} ] Hence, frac{x-2y{y} = -frac{7}{6}} is correct. Conclusion: The incorrect expression is Option C. The final answer is The incorrect expression, given the choices, is boxed{textbf{(C)} frac{3x+3y}{x} = frac{18}{5}}.