# SOLUTION: The second of three numbers is 7 less than 3 times the first. The third is 13 less than 6 times the first. If twice the first is decreased by the third, the result is -3. Find the

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: The second of three numbers is 7 less than 3 times the first. The third is 13 less than 6 times the first. If twice the first is decreased by the third, the result is -3. Find the      Log On

 Ad: Over 600 Algebra Word Problems at edhelper.com Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Mathway solves algebra homework problems with step-by-step help!

 Word Problems: Numbers, consecutive odd/even, digits Solvers Lessons Answers archive Quiz In Depth

 Question 159625: The second of three numbers is 7 less than 3 times the first. The third is 13 less than 6 times the first. If twice the first is decreased by the third, the result is -3. Find the three numbers.Answer by ankor@dixie-net.com(16525)   (Show Source): You can put this solution on YOUR website! The second of three numbers is 7 less than 3 times the first. The third is 13 less than 6 times the first. If twice the first is decreased by the third, the result is -3. Find the three numbers. : Let x = "the first number" Let y = "the second number" Let z = "the third number" : Write an equation for each statement: : 'The second of three numbers is 7 less than 3 times the first." y = 3x - 7 : " The third is 13 less than 6 times the first." z = 6x - 13 : "If twice the first is decreased by the third, the result is -3." 2x - z = -3 : Find the three numbers. : Note that the 2nd equation is: z = (6x-13), substitute this for z in the last equation: 2x - (6x-13) = -3 2x - 6x + 13 = -3; (removing the brackets, changes the sign of 13) 2x - 6x = -3 - 13 -4x = -16 x = x = +4 : Recall that z = 6x -13, substitute 4 for x z = 6(4) - 13 z = 24 - 13 z = 11 and y = 3x - 7; substitute 4 for x again y = 3(4) - 7 y = 12 - 7 y = 5 : : Check our solution in the statement: " If twice the first is decreased by the third, the result is -3. 2(4) - 11 = -3