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Write the following statement as an algebraic expression. There are c players on the school's football team. The team scored a total of 36 goals this season. One of the players, Jack, scored 2 more goals than the average per player. How many goals did Jack score?​

User Marqueone
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Answer:

36/c + 2

Explanation:

First, how do you find an average? By dividing some quantity by another quantity, of course. But you have to determine which to divide by which.

It makes sense that we'd want to know, on average, how many goals each player scored. And the 2nd-to-last sentence pretty much says that, "average [goals] per player."

You'd find that by dividing the number of goals by the number of players. Goals/players = goals per player

If they'd told us there were 12 people on the team, then it's easy: 36 goals ÷ 12 players = 3 goals per player

What if there were 18 players? Then it's just: 36 goals ÷ 18 players = 2 goals per player.

But they don't tell us exactly how many players there are, they assign it the variable 'c'. "Let c = # of players on the team."

So using 'c', how do we calculate the average goals per player? Simply by substituting 'c' where before we had a specific number:

Average goals per player = 36 goals ÷ 'c' players = 36/c

They tell us that Jack scored 2 more goals than that average, so we just add 2 to that term:

36/c + 2 = the average number of goals Jack scored

Going back to where I started, say there are 12 players on the team, and substitute that in for 'c':

36/12 + 2 = 3 + 2 = Jack scored 5 goals

Try it with 24:

24/2 + 2 = 2 + 2 = Jack scored 4 goals

It still works even if you don't get a whole number as an answer, because it's an average goals per game. Assume the team has 20 players:

36 goals ÷ 20 players means each player scored, on average, 1.8 goals per game. Jack scored 2 more goals than that average, so he scored 1.8 + 2 = 3.8 goals/game

User JonathanBristow
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