The sum of two numbers is 35; 1/2 of the smaller number is equal to 1/3 of the greater number. Find the numbers.

Question

The sum of two numbers is 35; 1/2 of the smaller number is equal to 1/3 of the greater number. Find the numbers.

Answer 1

Hi Salman,

 

Suppose smaller number =x, greater number=y.

 

x+y = 35  ....eq 1

 

x/2=y/3

 

so x= 2y/3.

Substituting the value of x in eq 1, we get

 

2y/3 + y=35

 

multiply eq by 3, we get

 

2y +3y = 105

5y=105

 

y=105/5 =21

x= 2y/3 = 2*21/3 =14

 

so two numbers are 14,21

 

you can check your answer, 1/2 of smaller number=14/2=7

                                         1/3 of greater number=21/3=7

Both are equal.

Answer 2

X is smaller number

 

Y is bigger number

 

X + Y = 35

 

(1/2)X = (1/3)Y

 

mutiply both sides by l.c.d., 6, to get rid of denominators

 

        3X = 2Y

 

  3X - 2Y = 0

 

     X + Y = 35  Multiply by 2

 

  2X + 2Y =70

 

combine with other equation

 

          5X =70

 

            X = 14

 

smaller number is 14

 

larger number is 21

 

 

 

   

Answer 3

Let x = the smaller number

Let y = the larger number

 

Use these variables to create the equation that represent the sum of the numbers and how the numbers relate to each other.

 

x + y = 35                   eq1

 

(1/2)x = (1/3)y            eq2

 

 

The second equation can be rearranged to have no denominators. If we cross-multiply, we get

 

2y = 3x                eq2

 

 

The bolded equations is a system of equations.  Use substitution/elimination method to solve for x and y.