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.

Question

With these Gobucks, users can purchase accessories for their avatars or buy special abilities.
1.) 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
a. What does constant 120 mean in the equation?
b. What does the variable x represent in the equation? Solve for x.
c. How much money will go to the children in the family?

Answer 1

Let's break down the questions one by one.

a. What does the constant 120 mean in the equation?

The constant 120 represents the amount of money allocated to the adults in the family for GoBucks. Specifically, it is the value that corresponds to \(\frac{2}{3}\) of the total budget for GoBucks.

b. What does the variable x represent in the equation? Solve for x.

The variable \(x\) represents the total budget for GoBucks. To solve for \(x\), we rearrange the equation \( \frac{2}{3} x = 120 \).

To solve for \(x\):

1. Multiply both sides of the equation by \(\frac{3}{2}\):

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

2. Calculate:

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

So, \(x = 180\). This means the total budget for GoBucks is $180.

c. How much money will go to the children in the family?

Since \(\frac{2}{3}\) of the budget goes to the adults, the remaining \(\frac{1}{3}\) goes to the children.

To find out how much money goes to the children, we can calculate:

\[ \text{Children's share} = \frac{1}{3} x = \frac{1}{3} \times 180 \]

Calculating this gives:

\[ \text{Children's share} = 60 \]

Thus, $60 will go to the children in the family for GoBucks.