The larger of two numbers is five more than three times the smaller. If their sum is 97, find the larger number.

Question

Please help.

Answer 1

Let:

     x = larger number

     y = smaller number

 

Translate:

  "larger of two numbers is five more than three times the smaller"     means

                     x              =   5         +          3    *        y                [eq1]

 

  "their sum is 97"      means

        x + y = 97                           [eq2]

 

  "find the larger number"     means

     Report the value of x.

 

The math:

     To find the value of x, let's use the two equations to make one equation with x (not y) in it.

     y = 97 - x             [from eq2]

     x = 5 + 3(97-x)       [substitute for y in eq2]

 

     x  = 5 + 291 - 3x             [distribute]

    4x = 296                       [add (3x to both sides]

    x = 74                           [divide both sides by 74]

     The larger number is 74.

 

O.K., you have answered the problem.  If you have time and want to have confidence in your work, check the result.

 

Check:

  Put x=74 into either eq1 or eq2 and solve for y.

     x + y = 97

      y = 97 - x

      y = 97 - 74

      y = 23

  Now, put y=23 into the other equation to see if it is true.

        Does        x = 5 + 3y    ?

                      74 = 5 + 3(23)    ?

                      74 = 5 + 69    ?

                      74 = 74    ?yes

Answer 2

Hi Andy,

 

You've posted a number of similar problems.  I will

set up the equations.  Try to solve them in the same

manner as already demonstrated.

 

If we let x be the larger number and y be the smaller number...

 

The larger of two numbers is five more than three times the smaller

x = 3y + 5  {equation 1}

x + y = 97  {equation 2}

 

Rearranged equation 1 to put variables on same side.

x - 3y = 5  

x + y = 97

 

Hint:  Subtract 2nd equation from the first to eliminate x.