Sarah Wilson was the top scorer in a women's professional basketball league for the 2006 regular season, with a total of 861 points. The number of two-point field goals that Sarah made was 65 less than double the number of three-point field goals she made. The number of free throws (each worth one point) she made was
33 less than the number of two-point field goals she made. Find how many free throws, two-point field goals, and three-point field goals Sarah Wilson made during
the 2006 regular season

9514 1404 393

Step-by-step explanation:

Let a, b, c represent the number of 1-point, 2-point, and 3-point goals, respectively.

  a +2b +3c = 861 . . . . . . total number of points

  b = 2c -65

  a = b -33

Substituting for a, then b, we have ...

  (b -33) +2b +3c = 861

  3b +3c = 894 . . . . . . . . . . add 33, collect terms

  b +c = 298 . . . . . . . . . . . . divide by 3

  (2c -65) +c = 298 . . . . . . substitute for b

  3c = 363 . . . . . . . . . . . . . add 65

  c = 121 . . . . . . . . . . . . . . . divide by 3

  b = 2(121) -65 = 177

  a = 177 -33 = 144

Sarah Wilson made ...

answer:     true

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."