Find two numbers whose difference is 10 and 1/6 of who sum is 11.

Question

Find two numbers whose difference is 10 and 1/6 of who sum is 11.

Answer 1

Michael J. read the problem this way:

  Find two numbers whose difference is ( 10 and 1/6 ) and whose sum is 11.

 

That's an example of why parentheses are first in the order of operations (remember P-E-M-D-A-S, Please Excuse My Dear Aunt Sally).

 

Let's read the problem this way:

   Find two numbers ( whose difference is 10 ) and ( 1/6 of whose sum is 11 ).

 

Wow, that's different !

 

Using x and y again,   the difference is  x - y = 10    and

          "of" means multiply                      (1/6)(x +y) = 11.

 

Now,  x + y  = 66

         x -  y   = 10

 

You may use the substitution method (solve for either x or y, then plug that in an the other equation to solve for y) or you may use the elimination method (I noticed that one equation as a (+y) and the other has a (-y), so let's just add the two equations -- we can do that because adding equations is adding equal amounts to both sides0.

 

        x + y + x - y  = 66 + 10

        2*x = 76

        x = 38

Now plug x into either equation to solve for y:

        38 + y = 66

        y = 66 - 38 = 28

 

Then, ALWAYS check your answer:

    Is the difference of 38 and 28 equal to 10?    YES !

    Is 1/6 of the sum of 38 and 28 equal to 11?     Well, you can add, then find 1/6 of the sum. Right?!

Answer 2

Let one number = x

Let the second number = y

 

 

Set up equations using the variables and info given. Since we have a mixed number, lets convert it to a fraction.

 

10 1/6 = 61 / 6

 

x + y = 11                eq1

x - y = 61 / 6            eq2

 

 

We can add the two equations to eliminate the y terms.

 

2x = 11 + (61 / 6)

2x = (66 + 61) / 6

2x = 127 / 6

  x = 127 / 12

 

Substitute this value of x into eq1

 

y = 11 - (127 / 12)

y = (132 - 127) / 12

y = 5 / 12

 

The two numbers are 127/12 and 5/12.