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### Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation2.4 Basic Operations With Variables - Word Problems - 4

 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 n2 = 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(n-1) 6 = n2 - n n2 - n - 6 = 0 is a quadratic equation with two values n = 3 and n= -2 Directions: Solve the unknown for the following word problems.
 Q 1: Six times the reciprocal of a number is equal to 24. What is the number? (Hint: 6 x 1/n = 24 that is same as 6/n = 24 Therefore n = _____)n = 5n = 4n = 1/4 Q 2: A number squared is equal to 81. Wwhat is the value? (Hint: n2 = 81)789 Q 3: Nine less than a number squared is equal to 16. If this number is positive, what is its value? (Hint: n2 - 9 = 16) 456 Q 4: The reciprocal of a number is equal to 1/9 of that number. If the number is positive, what is its value? (Hint: 1/n = n/9 Therefore n = ____)639 Q 5: Eight time the reciprocal of a number minus 2 is equal to 2. What is the number? (Hint: 8 x 1/n - 2 = 2 Therefore n = _____)n = 2n = 3n = 4 Q 6: The reciprocal of a number is equal to 1/16 of that number. If the number is positive, what is its value? (Hint: 1/n = n/16 Therefore n = ____)354 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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