The sum of two numbers is 24. If five times the smaller is added to twice the larger, the result is 78. Find the two numbers.

Question

Please help.

Answer 1

Hi Andy,

 

With the information given, we choose variables to

represent the two numbers and then set up equations

from the information given:

 

Let x = smaller number

Let y = larger number

 

The sum of two numbers is 24:

x + y = 24      {equation 1}

five times the smaller is added to twice the larger, the result is 78:

5x + 2y = 78  {equation 2}

 

We can solve by elimination or substitution.  Using elimination let's

multiply equation 1 by -2 and add the equations.  This will eliminate

the y variable, enabling us to solve for x.

 

-2x - 2y = -48

5x + 2y = 78

------------------

3x = 30

x = 10

 

x + y = 24

10 + y = 24

y = 14

 

Your numbers are 10, 14