This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To evaluate (a)/(x), we first convert the given ratios into fractions. Step 1: Convert ratios to fractional form. From a:b = 5:8, we have: (a)/(b) = (5)/(8) From x:y = 25:16, we have: (x)/(y) = (25)/(16) Step 2: Express a and x in terms of b and y respectively. From (a)/(b) = (5)/(8), we can write a: a = (5)/(8)b From (x)/(y) = (25)/(16), we can write x: x = (25)/(16)y Step 3: Substitute the expressions for a and x into (a)/(x). (a)/(x) = (5)/(8)b(25)/(16)y Step 4: Simplify the complex fraction. To simplify, multiply the numerator by the reciprocal of the denominator: (a)/(x) = (5)/(8)b × (16)/(25y) (a)/(x) = (5 × 16 × b)/(8 × 25 × y) Now, simplify the numerical part: (a)/(x) = (80b)/(200y) Divide both the numerator and the denominator of the numerical fraction by their greatest common divisor, which is 40: (a)/(x) = (80 ÷ 40)/(200 ÷ 40) · (b)/(y) (a)/(x) = (2)/(5) · (b)/(y) The expression for (a)/(x) is: (2b)/(5y) Send me the next one 📸