Question

Ethan's football team scored a total of 35 separate times this season with mix of touchdowns and field goals. Each touchdown is worth 7 points and each field goals is worth 3 points. the team scored a total of 193 points this season. Write the system and find how many touchdowns and field goals were scored.

Answer 1

Let,
touchdown = a
goal fields = b
1st condition,
a + b = 35 ......(1)
2nd condition,
7a + 3b = 193 .......(2)
Solving by substitution method,
From (1),
we get,
a = 35 - b ........(3)
Substituting (3) in (2),
we get,
7(35 - b) + 3b = 193
245 - 7b + 3b = 193
-7b + 3b = 193-245
-4b = -52
b = 52/4
b = 13 .......(4)
Substituting (4) in (3),
we get,
a = 35 - 13
a = 22
So the values are:
touchdown = a = 22
goal fields = b = 13



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