common core Algebra 1

Question

Find two consecutive even integers such that their sum is equal to the difference of three times the larger and two times the smaller

Answer 1

 

Let n = the smaller even integer

 

Then n + 2 = next consecutive even integer

 

From the problem statement:

    n + (n+2) = 3(n+2) - 2(n)

 

The left side is the sum of the two integers, the right side is 3*larger minus 2*smaller

 

Combine like terms:               2n+2 = n+6

Subtract n from both sides:      n+2 = 6

Subtract 2 from both sides:          n = 4 

 

                                n = 4  

                            n+2 = 6

 

Check:

           4 + 6 = 10

          3*6 - 2*4 = 18-8 = 10  (ok)