In this question, we have seven positive integers (p, q, r, s, t, u, and v). It's said that the sum of each group of three consecutive letters equals 35. Also, q+u=15.
So, by inference, we can conclude:
So, from the above, we can conclude that p+q+r=q+r+s. Thus:
From the above, we can also conclude that r+s+t=s+t+u. Thus:
Also, from the above, we see q+r+s=r+s+t. Thus, q=t.
Finally, we see that that s+t+u=t+u+v. Thus:
s = t+u-t-u+v
So, to go back to the original equation, we will perform substitutions.
Since r=u, we can write p+q+u=35
Since r=u and q+u=15, we can write q+u+s=35
To add all the positive integers, we get:
Remember that q+r+s=35. If s=20, then q+r=15
Remember also that t+u+v=35. If v=20 (remember v=s and s=20), then t+u=15
To add it all up, we get 20+15+20+15+20, which equals 90.