# Hockey teams goals

Hockey teams fired 200 goals. The second team was 13 less than the first team, the third 16 less than the first, and the fourth team had 19 goals less than the first. How many goals fired each team?

1.:  62
2.:  49
3.:  46
4.:  43

## Step-by-step explanation:

200=a+b+c+d
b= a-13
c = a- 16
d = a-19

a+b+c+d = 200
a-b = 13
a-c = 16
a-d = 19

Row 2 - Row 1 → Row 2
a+b+c+d = 200
-2b-c-d = -187
a-c = 16
a-d = 19

Row 3 - Row 1 → Row 3
a+b+c+d = 200
-2b-c-d = -187
-b-2c-d = -184
a-d = 19

Row 4 - Row 1 → Row 4
a+b+c+d = 200
-2b-c-d = -187
-b-2c-d = -184
-b-c-2d = -181

Row 3 - -1/-2 · Row 2 → Row 3
a+b+c+d = 200
-2b-c-d = -187
-1.5c-0.5d = -90.5
-b-c-2d = -181

Row 4 - -1/-2 · Row 2 → Row 4
a+b+c+d = 200
-2b-c-d = -187
-1.5c-0.5d = -90.5
-0.5c-1.5d = -87.5

Row 4 - -0.5/-1.5 · Row 3 → Row 4
a+b+c+d = 200
-2b-c-d = -187
-1.5c-0.5d = -90.5
-1.3333d = -57.3333

d = -57.33333333/-1.33333333 = 43
c = -90.5+0.5d/-1.5 = -90.5+0.5 · 43/-1.5 = 46
b = -187+c+d/-2 = -187+46+43/-2 = 49
a = 200-b-c-d = 200-49-46-43 = 62

a = 62
b = 49
c = 46
d = 43

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