Arrange a pattern

Question

There are 36 fifth graders in art class. The art teacher want to arrange their picture on the wall so that one is in the first row, two are in the second row, three are in the third row, etc. Write an equation to solve

Answer 1

When you add up a sequence of terms from 1 to n, the formula is:

 

Sum = n(n+1)

               2

 

If we set this equal to your goal of hanging 36 pictures, we get:

 

n(n+1)   = 36                      In wrote "1" under the 36 to make a proportion, which will speed us along. If you

    2            1                       cross-multiply the fractions you get...

 

1n(n+1)  = 2*36

n²+n       = 72                    Which means you have a quadratic equation. Get "0" on one side...

          -72   -72

n² + n -72 = 0                    And now you have to factor by un-FOILing:

(n + 9)(n - 8) = 0                Then use the Zero Factor Property to solve each factor...

n = -9 ,  n = 8                     Remember: although we did nothing, you can't have negative rows, so only "8" can be

the answer