Kyle wants to purchase 20 prefilled decorated eggs to set up an egg hunt for his nephews and nieces. Each egg is priced at $5.00, and the store offers two different incentives. Incentive 1: Purchase any set of 3 prefilled eggs for $12. Incentive 2: Take 20% off your entire purchase. Determine whether incentive 1 or incentive 2 offers a better discount. Find the discount amount. Round the answer to two decimal places as necessary. (1 point) Incentive offers a better discount. The discount amount of this incentive is $.

Answer 1

Let's calculate the total cost using both incentives to determine which one offers a better discount.

Incentive 1: Purchase any set of 3 prefilled eggs for $12.

1. Since Kyle wants to buy 20 eggs, we first calculate how many sets of 3 eggs he can buy and how many eggs will be left over:

   • He can buy \( \frac{20}{3} = 6 \) sets of 3 eggs (which totals 18 eggs) and will have 2 eggs left.

2. The cost for 6 sets of 3 eggs is: \[ 6 \text{ sets} \times $12/\text{set} = $72 \] The cost for the remaining 2 eggs at $5.00 each is: \[ 2 \text{ eggs} \times $5/\text{egg} = $10 \]

3. Therefore, the total cost with Incentive 1 is: \[ $72 + $10 = $82 \]

Incentive 2: Take 20% off your entire purchase.

1. The total cost without any discounts for 20 eggs at $5.00 each is: \[ 20 \text{ eggs} \times $5/\text{egg} = $100 \]

2. Now, we calculate 20% off the total cost: \[ 20% \text{ of } $100 = 0.20 \times 100 = $20 \] Therefore, the total cost with Incentive 2 after the discount is: \[ $100 - $20 = $80 \]

Compare the two incentives:

• Incentive 1 total cost: $82
• Incentive 2 total cost: $80

Conclusion:

Incentive 2 offers the better discount.

The discount amount of this incentive is \($20\).