Question 253348
find all sets of four consecutive odd integers whose sum is between 46 and 54

<pre><font size = 4 color = "indigo"><b>
x = 1st odd integer
x+2 = 2nd odd integer
x+4 = 3rd odd integer
x+6 = 4th odd integer

{{{46< x + (x+2)+(x+4)+(x+6)<54}}}

{{{46< x + x+2+x+4+x+6<54}}}

{{{46<4x + 12<54}}}

Subtract 12 from all three sides

{{{34<4x<42}}}

Divide through by 4

{{{34/4<x<42/4}}}

{{{8.5<x<10.5}}}

The only odd integer x between 8.5 and 10.5 is 9.

So there is just one set:

x = 1st odd integer = 9
x+2 = 2nd odd integer = 11
x+4 = 3rd odd integer = 13
x+6 = 4th odd integer = 15
sum = 9+11+13+15=48

Edwin</pre>