Problem
Undoing the average, 395 x 4 = 1580 phones across the four quarters.
If four numbers level off to 395 each, all four together must be four 395s — undoing the 'divide by 4' that made the average.
6.SP.A.3Work BackwardsTake away the two quarters we already know, Q1 = 450 and Q3 = 410, from the total. What is left is the combined sales of Q2 and Q4.
The whole is the sum of its parts; remove the known parts and the two unknown quarters are what remain.
6.SP.B.5Identify SubproblemsQ2 is 80 below Q4, so 2 x Q4 - 80 = 720 gives 2 x Q4 = 800 and Q4 = 400.
If the two quarters differ by 80 and add to 720, give the smaller one its missing 80 first, then split the even amount in half.
6.EE.B.7Identify SubproblemsThe two unknown quarters add to 720 and differ by 80, so twice the larger one is 720 plus 80.
Writing the smaller quarter as the larger one less 80 turns their sum into two copies of the larger with 80 taken away.
Adding that 80 back restores the two equal copies, and halving then leaves just one of them.
An average is a total in disguise — multiply it back up, subtract what you know, then split the rest by the gap.