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(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

(2)/(3)x=120

explain the steps short

3 answers

To find the total budget \( x \) for GoBucks using the equation \( \frac{2}{3}x = 120 \), follow these steps:

  1. Identify the equation: You have \( \frac{2}{3}x = 120 \).

  2. Isolate \( x \): To solve for \( x \), multiply both sides of the equation by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \).

    \[ x = 120 \times \frac{3}{2} \]

  3. Calculate the right side:

    \[ x = 120 \times 1.5 = 180 \]

  4. Conclusion: The total budget \( x \) for GoBucks is \( 180 \).

explain 3 more tell me what you know

Sure! Here are three more explanations related to the budgeting problem, focusing on different aspects:

1. Understanding Proportions:

  • The equation \( \frac{2}{3}x = 120 \) implies that \( \frac{2}{3} \) of the total budget \( x \) goes to the adults. This means that for every 3 parts of the budget, 2 parts are allocated to the adults. The remaining \( \frac{1}{3} \) of the budget (which is not shown in the equation) goes to the children.

2. Breaking Down the calculated Budget:

  • Once we determined that the total budget \( x = 180 \):
    • The amount allocated to adults can be calculated as \( \frac{2}{3} \times 180 = 120 \).
    • The remaining amount for children, which is \( \frac{1}{3} \) of the budget can be calculated as \( \frac{1}{3} \times 180 = 60 \).
    • Therefore, in this budget scenario, adults receive \( 120 \) and children receive \( 60 \).

3. Real-World Application:

  • This equation can be useful in real-world situations where you need to allocate a budget among different groups. For example, if a family is planning their monthly expenses, knowing how much goes to adults versus children can help in planning for necessities like groceries, education, entertainment, and savings. By setting up similar equations, families can effectively manage their finances and ensure that funds are allocated according to their needs.

These explanations should provide you with a deeper understanding of the budgeting problem and its implications!