# MATH - Find the Numbers - Word Problem

by SHERYL
(GA)

Solve the following problem. Be sure to show all steps (V.E.S.T.) and work in order to receive full credit.

The sum of three numbers is 26. The second number is twice the first and the third number is 6 more than the second. Find the numbers.

### Comments for MATH - Find the Numbers - Word Problem

 Aug 18, 2011 Linear Equations – 3 Variables - Word Problem by: Staff The question: by SHERYL (GA) Solve the following problem. Be sure to show all steps (V.E.S.T.) and work in order to receive full credit. The sum of three numbers is 26. The second number is twice the first and the third number is 6 more than the second. Find the numbers. The answer: The sum of three numbers is 26. x + y + z = 26 The second number is twice the first . . . y = 2x . . . the third number is 6 more than the second. z = y + 6 ---------------------------- Rewrite the equation for z in terms of x by substituting 2x for y (since y = 2x) z = y + 6 z = 2x + 6 ---------------------------- Rewrite the first equation entirely in terms of x (since y = 2x and z = 2x + 6) x + y + z = 26 x + (2x) + (2x + 6) = 26 x + 2x + 2x + 6 = 26 ---------------------------- Solve for x (x + 2x + 2x) + 6 = 26 (5x) + 6 = 26 5x + 6 = 26 5x + 6 - 6 = 26 - 6 5x + 0 = 26 - 6 5x = 26 – 6 5x = 20 5x/5 = 20/5 (5/5)*x = 20/5 (1)*x = 20/5 x = 20/5 x = 4 ---------------------------- Solve for y y = 2x y = 2*4 y = 8 ---------------------------- Solve for z z = 2x + 6 z = 2*4 + 6 z = 8 + 6 z = 14 ---------------------------- the final answer is: x = 4, y = 8, z = 14 check the solution by substituting the numerical values of x, y, and z into the original equation x + y + z = 26 4 + 8 + 14 = 26 26 = 26, OK → x = 4, y = 8, z = 14 are valid solutions Thanks for writing. Staff www.solving-math-problems.com