Total Points scored

Question

Each quarter Lisa scores two less than twice the number of points she scored in the previous quarter. If she scored 26 points in the fourth quarter, how many points did she score in the entire game? Assuming game did not go into overtime.

Answer 1

Hi Nicole.

Lisa ultimately scored 53 points: 5 (Q1), 8 (Q2), 14 (Q3) and 26 (Q4--given). Starting with 26 points in the 4th quarter (Q4) and working backwards, using the expression verbalized in the opening statement (2x-2), each of the previous quarter's points Lisa scored were found:

2x - 2 = 26; 2x - 2 + 2 = 26 + 2; 2x = 28; 2x/2 = 28/2; x = 14 for the 3rd quarter (Q3);

2x - 2 = 14; 2x - 2 + 2 = 14 + 2; 2x = 16; 2x/2 = 16/2; x = 8 for the 2nd quarter (Q2); and

2x - 2 = 8; 2x - 2 + 2 = 8 + 2; 2x = 10; 2x/2 = 10/2; x = 5 for the 1st quarter (Q1).

5 + 8 + 14 +26 = 53 total points