A family can buy GoBucks. With these Gobucks, users can purchase accessories for their avatars or buy special abilities. The following represents the GoBucks packages available for purchase and the amount of in-game coins the packages provide. The second table displays the accessories they can purchase:

Question

Table 1:
Cost: $5: Coin Packages: 400 Coins
Cost: $10: Coin Packages: 800 Coins
Cost: $20: Coin Packages: 1,700 Coins
Cost: $50: Coin Packages: 4,500 Coins
Cost: $100: Coin Packages: 10,000 Coins
Table 2:
Level 1 Accessories: Cost: 250 Coins
Level 2 Accessories: Cost: 320 Coins
Level 3 Accessories: Cost: 500 Coins
Level 4 Accessories: Cost: 730 Coins
Level 5 Accessories: Cost: 1225 Coins
A. Two children used their allowance money to go with their budgeted amount for their GoBucks. Create and solve an equation that represents the allowance amount if they each have $50 to spend.
B. Determine two possible package options for one of the children based on the $50 budget. Create and solve an equation that represents the number of Level 3 accessories they could purchase for each package option.

Answer 1

Part A: Creating and Solving the Equation for Allowance Amount

Assuming that both children have their individual budgets of $50, we can represent the total allowance amount (A) for each child as:

\[ A = 50 \]

Since both children have this fixed amount of money, there’s no further calculation needed for the allowance amount, as it is simply:

\[ A = 50 \text{ dollars} \]

Part B: Determining Package Options and Solving for Level 3 Accessories

Package Options Based on the $50 Budget

Looking at the available GoBucks packages from Table 1, we see:

• Cost: $50 provides 4,500 Coins.

Since the budget is exactly $50, the only package they can buy is:

• Package Option 1: $50 package which gives 4,500 Coins.

To explore another option, they can choose to spend less than $50:

• Cost: $20 provides 1,700 Coins.
• Cost: $10 provides 800 Coins.
• Cost: $5 provides 400 Coins.

We can choose the following combination of packages as a second option:

• Package Option 2: Buy one $20 package and one $10 package, which would give:
  • Package $20 = 1,700 Coins
  • Package $10 = 800 Coins
  • Total coins = 1,700 + 800 = 2,500 Coins
  • Total cost = 20 + 10 = $30

Calculate the Number of Level 3 Accessories They Can Purchase

Level 3 Accessories Cost

From Table 2, Level 3 accessories cost 500 Coins.

1. For Package Option 1 (4,500 Coins): \[ \text{Number of Level 3 Accessories} = \frac{4,500 \text{ Coins}}{500 \text{ Coins/accessory}} = 9 \text{ accessories} \]

2. For Package Option 2 (2,500 Coins): \[ \text{Number of Level 3 Accessories} = \frac{2,500 \text{ Coins}}{500 \text{ Coins/accessory}} = 5 \text{ accessories} \]

Summary

• Allowance Amount: $50 for each child.
• Package Options:
  • Option 1: $50 package (4,500 Coins) - can buy 9 Level 3 accessories.
  • Option 2: $20 package + $10 package ($30 total, 2,500 Coins) - can buy 5 Level 3 accessories.