Problem Solving

Question

The larger of two numbers is two more than three times the smaller.And when the larger number is subtracted from the smaller, the result is -16. What are the two numbers.

Answer 1

x = larger number

y = smaller number

 

The larger number of two numbers (x) is (=) two more (2 +) than three time (3X) the smaller (y).

x = 2 + 3y

When the larger number (x) is subtracted (- before the x) from the smaller (y), the result is (=) -16.

y - x = -16

Now that we have created two equations in two variables, we can solve the equations for the answer.  I will used substitution.

y - x = -16                               Equation 2

y - (2 + 3y) = -16                     Substitute the value of x in equation 1 for x in equation 2

y - 2 - 3y = -16                         Distributive property

-2y - 2 = -16                             Simplify

-2y - 2 + 2 = -16 + 2                 Add 2 to each side

- 2y = -14                                 Simplify

-2y/(-2) = -14/(-2)                     Divide each side by -2

y = 7                                        Simplify

x = 2 + 3y                                  Equation 1

x = 2 + 3(7)                               Substitution

x = 2 + 21                                  Simplify

x = 23

The larger number is 23 and the smaller number is 7.