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:
2/3 x = 120

Answer 1

To solve for the total budget \( x \) for GoBucks, we need to rearrange the equation you provided:

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

To isolate \( x \), we'll multiply both sides of the equation by the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\):

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

Calculating the right side:

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

Thus, the total budget for GoBucks is \( \textbf{180} \).

To further break it down:

• The amount allocated to the adults in the family (which is \( \frac{2}{3} \) of the budget) would be: \[ \frac{2}{3} \times 180 = 120 \]

• The amount allocated to the children (which is \( \frac{1}{3} \) of the budget) would be: \[ \frac{1}{3} \times 180 = 60 \]

In summary:

• Total budget \( x = 180 \)
• Budget for adults = 120
• Budget for children = 60