Ball game

Richard, Denis, and Denise together scored 932 goals. Denis scored four goals over Denise, but Denis scored 24 goals less than Richard. Determine the number of goals for each player.

Correct answer:

d =  304
r =  328
s =  300

Step-by-step explanation:


r+d+s = 932
d = 4 + s
d = r - 24

d+r+s = 932
d-s = 4
d-r = -24

Row 2 - Row 1 → Row 2
d+r+s = 932
-r-2s = -928
d-r = -24

Row 3 - Row 1 → Row 3
d+r+s = 932
-r-2s = -928
-2r-s = -956

Pivot: Row 2 ↔ Row 3
d+r+s = 932
-2r-s = -956
-r-2s = -928

Row 3 - -1/-2 · Row 2 → Row 3
d+r+s = 932
-2r-s = -956
-1.5s = -450


s = -450/-1.5 = 300
r = -956+s/-2 = -956+300/-2 = 328
d = 932-r-s = 932-328-300 = 304

d = 304
r = 328
s = 300

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