
Example 1: The reciprocal of a number is equal to 1/25 of that number. If the number is positive, what is its value? Translate the statement to a math equation, and then solve the equation. Let the number be n "The reciprocal of a number" translates to 1/n. "Is equal to 1/25 of that number" translates to 1/9 x n = n/9 Therefore the equation is 1/n = n/25 Solving for n we get: 1/n = n/25 n^{2} = 25 n = 5 Example 2: Six times the reciprocal of a number is equal to that number decreased by 1. What is the number? Solution: Translate the statement to a math equation, and then solve the equation. Let the number be n. Its reciprocal is 1/n. Six times the reciprocal of a number translates to 6 x 1/n = 6/n That number decreased by 1" translates to n  1 Therefore the equation is 6/n = n  1 Solving the equation to get the value of n: 6/n = n  1 6/n = (n  1)/1 6(1) = n(n1) 6 = n^{2}  n n^{2}  n  6 = 0 is a quadratic equation with two values n = 3 and n= 2 Directions: Solve the unknown for the following word problems. 