Hockey teams goals

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

Correct answer:

1.:  62
2.:  49
3.:  46
4.:  43

Step-by-step explanation:

200=a+b+c+d b=a13 c=a16 d=a19  200=a+(a13)+(a16)+(a19) 200=4a48 248=4a a=62 b=a13=49 c=a16=46 d=a19=43

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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