The sum of two numbers is 103 .The larger number is 1 more than five times the smaller number. find the numbers .

Question

Solve each of the following problems by setting up and solving an algebraic equation.

Answer 1

We have 2 unknowns, so we must have 2 equations to solve.

Let x=the smaller number

     y=the larger number

Eq. I:   x+y=103

Eq. II:  y=5x+1

You can use either the substitution or elimination methods to solve this. Let's use the substitution method with the value of y from Eq. II in Eq. I and solve for x:

           x+y=103                Eq. I

           x+5x+1=103          substituting y from Eq. II

           x+5x=103-1           subtract 1 from both sides to isolate the x terms

           6x=102                  simplify

           x=102/6                divide both sides by 6 to isolate x

           x=17

Using this value for x in Eq. II, we can solve for y:

          y=5x+1             Eq. II

          y=5(17)+1        substitute 17 for x

          y=85+1            

          y=86

The 2 numbers are 17 & 86.