Question

In a hockey tournament, the seals scored 3 less than twice as many points as the fins scored. The rays scored 2 more points than the fins. All together, there were 11 total goals scored by the three teams. Let x represent the number of points scored by the fins. Which equation can be used to find the value of x and how many points did each team score?

1) x(x - 3)(2x) = 11; Fins: 4 points, Seals: 1 point, Rays: 6 points
2) x(2x - 3)(x + 2) = 11; Fins: 3 points, Seals: 3 points, Rays: 5 points
3) x(2x - 3)(x - 2) = 11; Fins: 4 points, Seals: 5 points, Rays: 2 points
4) x(x + 3)(x - 2) = 11; Fins: 2 points, Seals: 5 points, Rays: 4 points

Answer 1

2) x(2x - 3)(x + 2) = 11; Fins: 3 points, Seals: 3 points, Rays: 5 points

Step-by-step explanation:

Answer 2

The correct equation to find the number of points scored by the Fins (x) in the hockey tournament is x(2x - 3)(x + 2) = 11. Solving this, we determine that the Fins scored 3 points, the Seals scored 3 points, and the Rays scored 5 points.

Step-by-step explanation:

The question is about solving a problem involving algebraic expressions to determine the number of points scored by each of the three teams in a hockey tournament. To find the value of x, which represents the number of points scored by the Fins, we can set up an equation based on the information provided:

• The Seals scored 3 less than twice as many points as the Fins: 2x - 3
• The Rays scored 2 more points than the Fins: x + 2
• All together, there were 11 total goals scored: x + (2x - 3) + (x + 2) = 11

Now we can combine the terms to create a single equation that we can solve for x:

4x - 1 = 11

Adding 1 to both sides gives us 4x = 12, and dividing both sides by 4 gives us x = 3. Therefore, the number of points scored by the Fins is 3. We can now substitute x into the expressions for the Seals and Rays to find their scores:

• Seals: 2(3) - 3 = 3 points
• Rays: 3 + 2 = 5 points

The correct answer is option 2, which suggests the equation to find x is x(2x - 3)(x + 2) = 11 and the points scored by the teams are Fins: 3 points, Seals: 3 points, Rays: 5 points.