The sum of two numbers are 24. 7 times the smaller number is the same as 5 times the larger number

Question

We need help with an algebra word problem

Answer 1

Let X = small number and let Y = large number

 

From the words in the problem we can get 2 equations

 

    X + Y = 24

 

     7X = 5Y        Solve the first equation for X

 

     X = 24 - Y     Now that this phrase for X (24 - Y) and replace X in the second equation

 

7(24 - Y) = 5Y         distribute

 

168 - 7Y = 5Y          add 7Y to both sides

 

        168 = 12Y       divide both sides by 12

 

          14 = Y         Now find X using the first equation (X + Y = 24

 

      X + 14 = 24

 

           X = 10

 

CHECK

 

7(10) = 5(14)

 

  70 = 70√