Function of the Day: There is a family who loves to play video games. The family plays an app that allows users to play a wide variety of games and talk to each other online called GoBlocks. The family can build together, play together, and purchase in-game accessories to personalize their avatars. The application is free but there are in-app purchases with the help of GoBucks. With these Gobucks, users can purchase accessories for their avatars or buy special abilities.

Question

2/3 of the budget for GoBucks goes to the adults in the family and the rest goes to the children in the family. The total budget can be calculated using the following modeled equation:
23x = 120

What do you know about each number in the equation and x in the equation?
Give me 10 things

Answer 1

Certainly! Let's dissect the equation \( 23x = 120 \) and uncover its components and implications:

1. Definition of the Variable: In the equation, \( x \) represents the amount of money allocated to each unit of GoBucks. This is what we want to solve for.

2. Total Budget: The total budget for GoBucks is 120 units (which could represent dollars, for example).

3. Coefficient Interpretation: The number 23 is the multiplier that relates \( x \) to the total budget. It indicates how many units of GoBucks are allocated per dollar.

4. Proportionality: The equation suggests a proportional relationship, where the total allocation (120) is distributed based on the value of \( x \).

5. Solving for \( x \): To find the value of \( x \), you would divide both sides of the equation by 23: \( x = \frac{120}{23} \).

6. Calculating \( x \): When you calculate \( x \), you find that \( x \approx 5.217 \). This means that each individual unit of GoBucks (as defined by \( x \)) is worth roughly 5.22 units of currency.

7. Distribution of Funds: Given that two-thirds (or approximately 66.67%) of the budget (120) goes to the adults, the adults receive \( \frac{2}{3} \times 120 \approx 80 \). The children receive the remaining \( \frac{1}{3} \times 120 \approx 40 \).

8. Budget Composition: Thus, we can interpret that the adults have a budget of approximately 80 GoBucks for accessories or abilities, while the children have approximately 40 GoBucks.

9. Applying In-App Purchases: The result for \( x \) can help determine how many purchases or accessories each family member can afford based on the price of each item in GoBucks.

10. Real-World Relevance: This equation could reflect a family’s budgeting strategy, showcasing how they allocate their gaming expenses according to roles (adults vs. children) while purchasing in-game items or enhancements.

These points clarify both the mathematical structure of the equation, as well as its practical implications in the context of family spending on gaming.

Answer 2

Give me 15 and make it 6th grade-like

Answer 3

Sure! Here are 15 simpler explanations about the equation \( 23x = 120 \) that would be suitable for a 6th grader:

1. What is the Equation?: The equation \( 23x = 120 \) is a math problem where we want to find out what \( x \) is.

2. Finding \( x \): \( x \) represents how much money one GoBuck is worth.

3. Total Budget: The total amount of GoBucks the family has is 120 (pretend it's dollars).

4. Understanding 23: The number 23 tells us that we are looking at 23 parts of the total budget when we consider the value of \( x \).

5. Dividing the Budget: To find out how much one GoBuck is worth, we divide 120 by 23.

6. Solving for \( x \): If you solve it, you find that \( x \) is about 5.22. So, one GoBuck is worth about 5.22 dollars!

7. Adult and Child Shares: The family divides their money so that 2/3 of the budget goes to adults and 1/3 goes to kids.

8. Calculating Adult Amount: If adults get 2/3 of 120, they would have about 80 GoBucks to spend.

9. Calculating Child Amount: The kids would get 1/3 of 120, which is around 40 GoBucks to spend.

10. How Much Can They Buy?: If a game accessory costs 5 GoBucks, the adults could buy about 16 items (80/5) and the kids could buy about 8 items (40/5).

11. Understanding Proportions: The equation shows how the total budget for GoBucks is split up based on the number 23.

12. Meaning of \( 23x \): The left side of the equation (23 times \( x \)) means if you take the value of one GoBuck (x) and multiply it by 23, you should get the total amount of money.

13. Real-Life Application: This equation is helpful for families to budget their money for fun games and buying cool things.

14. Learning Division: Solving this equation teaches you how to divide and understand proportions, which is important in math.

15. Fun with Math: Knowing how to solve equations like this can help you play games more wisely, as you learn to manage your money and resources better!

These points give a clear, fun explanation of the equation and how it relates to the budget for GoBucks in a way that is understandable for a 6th grader.