# Math - Solve Word Problem

by Czyrell May Ebe
(Batangas City)

The larger of two numbers is six more than six times the smaller number. The larger number is also one hundred twenty-two more than two times the smaller number. What are the numbers?

Let l be the larger number
Let s be the smaller number

### Comments for Math - Solve Word Problem

 Jul 15, 2011 Solve Word Problem by: Staff The question: by Czyrell May Ebe (Batangas City) The larger of two numbers is six more than six times the smaller number. The larger number is also one hundred twenty-two more than two times the smaller number. What are the numbers? Let l be the larger number Let s be the smaller number The answer: L = large number S = small number The larger of two numbers is six more than six times the smaller number. L = 6S + 6 The larger number is also one hundred twenty-two more than two times the smaller number. L = 2S + 122 We now have two equations with two unknowns: L = 6S + 6 L = 2S + 122 Solve for the variable “S” using the addition/subtraction method. Eliminate the unknown variable “L” by subtracting the second equation from the first equation: L = 6S + 6 -(L = 2S + 122) L = 6S + 6 -L = -2S - 122 ------------------ L - L = 6S - 2S + 6 - 122 0 = 6S - 2S + 6 - 122 0 = 4S + 6 – 122 0 = 4S -116 Add 116 to each side of the equation 0 = 4S -116 0 + 116 = 4S -116 + 116 116 = 4S -116 + 116 116 = 4S + 0 116 = 4S To eliminate the 4 from the 4S, divide each side of the equation by 4 4S = 116 4S/4 = 116/4 S*(4/4) = 116/4 S*(1) = 116/4 S = 116/4 S = 29 Solve for “L” by substituting the numerical value of “S” (S = 29) into either one of the original equations L = 6S + 6 L = 6*29 + 6 L = 174 + 6 L = 180 The final answer is: S (the smaller number) = 29; L (the larger number) = 180 Check the work. Substitute the numerical values of both S and L in the original equations: L = 6S + 6 180 = 6*29 + 6 180 = 174 + 6 180 = 180, OK L = 2S + 122 180 = 2*29 + 122 180 = 58 + 122 180 = 180, OK Thanks for writing. Staff www.solving-math-problems.com