Finding the Minimum Number of Points Janelle Needs to Score

Oct 13, 2025 by miodeya.com 69 views

In a Beanbag Toss Game: Solving for Janelle's Victory

In a game of beanbag toss, Janelle is on a mission to score more than 50 points to emerge victorious. The game involves two types of targets: round and square. Landing on a round target awards Janelle 5 points, while landing on a square target awards her 8 points. To determine the number of times Janelle needs to land on each target to achieve her goal, we can use algebraic equations to solve for the unknown variables.

Let's break down the problem and understand what's required. Janelle needs to score more than 50 points, and she can achieve this by landing on either the round or square targets. We can represent the number of times Janelle lands on the round target as x and the number of times she lands on the square target as y.

To solve for Janelle's victory, we need to set up an equation that represents the total points she scores. Since landing on a round target awards 5 points and landing on a square target awards 8 points, we can write the equation as:

5x + 8y > 50

This equation represents the total points Janelle scores, where x is the number of times she lands on the round target and y is the number of times she lands on the square target.

To solve for x and y, we need to find the values that satisfy the equation 5x + 8y > 50. Since we're looking for the minimum number of points Janelle needs to score, we can set up the equation as an inequality.

5x + 8y > 50

We can start by finding the minimum value of x that satisfies the equation. Since x represents the number of times Janelle lands on the round target, it must be a non-negative integer.

Finding the Minimum of x

To find the minimum value of x, we can start by setting x = 1 and solving for y.

5(1) + 8y > 50

Simplifying the equation, we get:

5 + 8y > 50

Subtracting 5 from both sides, we get:

8y > 45

Dividing both sides by 8, we get:

y > 5.625

Since y must be a non-negative integer, the minimum value of y that satisfies the equation is y = 6.

Finding the Minimum Value of x (Continued)

Now that we have the minimum value of y, we can substitute it back into the equation to find the minimum value of x.

5x + 8(6) > 50

Simplifying the equation, we get:

5x + 48 > 50

Subtracting 48 from both sides, we get:

5x > 2

Dividing both sides by 5, we get:

x > 0.4

Since x must be a non-negative integer, the minimum value of x that satisfies the equation is x = 1.

Finding the Minimum Number of Points Janelle Needs to Score

Now that we have the minimum values of x and y, we can substitute them back into the equation to find the minimum number of points Janelle needs to score.

5(1) + 8(6) = 5 + 48 = 53

Therefore, the minimum number of points Janelle needs to score to win is 53.

In conclusion, Janelle needs to land on the round target at least 1 time and the square target at least 6 times to score more than 50 points. The minimum number of points Janelle needs to score to win is 53.

The final answer is $\boxed{53}$ .
In a Beanbag Toss Game: Solving for Janelle's Victory - Q&A

In our previous article, we explored the problem of Janelle scoring more than 50 points in a game of beanbag toss. We set up an equation to represent the total points she scores and solved for the minimum number of points Janelle needs to score to win. In this article, we'll answer some frequently asked questions related to the problem.

Q: What is the minimum number of points Janelle needs to score to win?

A: The minimum number of points Janelle needs to score to win is 53.

Q: How many times does Janelle need to land on the round target to score more than 50 points?

A: Janelle needs to land on the round target at least 1 time to score more than 50 points.

Q: How many times does Janelle need to land on the square target to score more than 50 points?

A: Janelle needs to land on the square target at least 6 times to score more than 50 points.

Q: What is the equation that represents the total points Janelle scores?

A: The equation that represents the total points Janelle scores is 5x + 8y > 50, where x is the number of times Janelle lands on the round target and y is the number of times she lands on the square target.

Q: What is the significance of the inequality in the equation?

A: The inequality in the equation represents the fact that Janelle needs to score more than 50 points to win.

Q: How can we use the equation to find the minimum number of points Janelle needs to score?

A: We can use the equation to find the minimum number of points Janelle needs to score by setting x = 1 and solving for y. We can then substitute the value of y back into the equation to find the minimum number of points Janelle needs to score.

Q: What is the minimum value of x that satisfies the equation?

A: The minimum value of x that satisfies the equation is x = 1.

Q: What is the minimum value of y that satisfies the equation?

A: The minimum value of y that satisfies the equation is y = 6.

In conclusion, we've answered some frequently asked questions related to the problem of Janelle scoring more than 50 points in a game of beanbag toss. We've also provided a step-by-step solution to the problem and explained the significance of the inequality in the equation.

The final answer is $\boxed{53}$ .