half the difference between two numbers is two. the sum of the greater number and twice the smaller is 13

Question

find both  numbers

Answer 1

This is a word problem so the solution is to set up equations to solve for the numbers which we will call x and y.

 

The first part says half the difference between two numbers is two. Difference implies subtraction. So 

 

           (1/2)(x-y)=2 will be our first equation (1).

 

The second part says sum of the greater number and twice the smaller. We will say x is greater than y, and sum implies addition and twice implies multiplication. So

           

          x+2y=13 is our second equation (2). Now we just have to solve for x and y.

 

A shortcut is to multiply equation1 by the number 2 yielding x-y=4

Now we have:   x+2y=13           and we can simplify by multiplying the bottom eq by -1 and adding the two equations

                 +[-1(x - y)=-1(4)]

 

This yields: 3y=9 and solving for y: y=9/3 = 3! now we have y = 3, we can use it to solve for x in eq 1

 

(1/2)(x-3)=2

x-3=4, and x =4+3 = 7! so x =7

 

Finally we must check our work:

      (1/2)(7-3)=2 check

      7+2(3)=13   check

 

Hope that helps!