In a game, the Bulls score a total of 103 points and made three times as many field goals (2 points each) as free throws (1 point each). They also made eleven 3 points. How many goals did they have?
103=3(2)+ 1 + 11(3)
would this equation be right?
No, that is not right.
Let the number of free throws be x.
There are 3x two-point field goals, and 11 from "downtown" (3 pointers).
103 = 11*3 + 2*(3x) + x
70 = 7x
x = 10 free throws
3x = 30 is the number of two-point "field goals"
To determine the number of field goals made by the Bulls, let's break down the information given:
1. Field goals score 2 points each.
2. Free throws score 1 point each.
3. The Bulls made three times as many field goals as free throws.
4. The Bulls made eleven 3-point shots.
To calculate the number of field goals made, we can assign variables:
Let x be the number of free throws made.
Then, the number of field goals made would be 3x since they made three times as many field goals as free throws.
Since each field goal is worth 2 points and each free throw is worth 1 point, the equation representing the total points scored can be set up as follows:
Total Points = (2 points per field goal) * (number of field goals) + (1 point per free throw) * (number of free throws) + (3 points per 3-point shot) * (number of 3-point shots)
Now let's substitute the values into the equation:
103 = (2 * 3x) + (1 * x) + (3 * 11)
Simplifying the equation:
103 = 6x + x + 33
Combine like terms:
103 = 7x + 33
Subtract 33 from both sides:
70 = 7x
Divide both sides by 7:
10 = x
Therefore, the number of free throws made by the Bulls is 10. Since they made three times as many field goals, the number of field goals made is:
3x = 3 * 10 = 30
Therefore, the Bulls made 30 field goals.