Algebra House
  • Ask a Question
    • Answered Questions
  • Examples
  • State Test Practice
    • Algebra 1 State Test Practice
    • Geometry State Test Practice
  • ACT and SAT
  • Calculators
    • Problem Solver
    • Graphing Calculator
    • 3D Graphing Calculator
  • Contact
    • Contact Algebra House
    • Leave a Tip


​​ALGEBRA eXAMPLES

Find the two numbers given their difference and their product

12/4/2017

 
Find two positive numbers whose difference is 27 and whose product is 2680.
​

x = one positive number 
y = other positive number 


x - y = 27    {their difference is 27}
xy = 2680    {their product is 2680}

x - y = 27    {the first equation}
x = y + 27    {added y to each side}

xy = 2680    {the second equation}
(y + 27)y = 2680    {substituted (y + 27), in for x, into second equation}
y² + 27y = 2680      {used the distributive property}
y² + 27y - 2680 = 0    {subtracted 2680 from each side}
(y + 67)(y - 40) = 0    {factored  into two binomials}
y + 67 = 0   or   y - 40 = 0    {set each factor equal to zero}
y = -67   or   y = 40    {solved each equation for x}

Using only the positive number, 40.

x = y + 27   {first equation, re-arranged}
x = 40 + 27   {substituted 40, in for y, into (y + 27)}
x = 67   {added}

40 and 67 are the two numbers 

​Ask Algebra House
​

Comments are closed.

    Ask a Question





    Examples

    All
    All Word Problems
    Basic Math
    Combining Like Terms
    Distributive Property
    Equations Of Lines
    Exponents
    Factoring
    Foil Method
    Functions
    Geometry
    Graphing
    Imaginary Numbers
    Inequalities
    Linear Equations
    Literal Equations
    Miscellaneous
    Percents
    Pythagorean Theorem
    Quadratic Equations
    Radicals
    Simplifying
    Slopes And Intercepts
    Solving Equations
    System Of Equations
    Word Problems Age
    Word Problems Distance
    Word Problems Geometry
    Word Problems Integers
    Word Problems Misc.
    Word Problems Mixture
    Word Problems Money
    Word Problems Number



Algebra House
  • Ask a Question
    • Answered Questions
  • Examples
  • State Test Practice
    • Algebra 1 State Test Practice
    • Geometry State Test Practice
  • ACT and SAT
  • Calculators
    • Problem Solver
    • Graphing Calculator
    • 3D Graphing Calculator
  • Contact
    • Contact Algebra House
    • Leave a Tip