GED Math: Calculating Overall Car Insurance Discount with Sequential Percentages

Understanding Sequential Discounts

• 💡 The problem involves calculating the overall percent change of a car insurance bill after two sequential discounts: a 20% good student discount and a 10% safe driver discount.
• ⚠️ Simply adding the percentages (20% + 10% = 30%) is incorrect because the discounts are applied in sequence, not all at once.

Step-by-Step Calculation

• 🎯 To solve, we can assume an original price for the car insurance bill; $300 is chosen for this example.
• 💰 After the first 20% discount, the price becomes $300 * (1 - 0.20) = $300 * 0.80 = $240.
• 📉 Applying the subsequent 10% discount to the new price: $240 * (1 - 0.10) = $240 * 0.90 = $216.

Determining Overall Percent Change

• 📊 The overall percent change is calculated using the formula: (New Price - Original Price) / Original Price * 100%.
• 📈 Substituting the values: ($216 - $300) / $300 * 100% = -$84 / $300 * 100% = -28%.
• ✅ The overall percent change in the car insurance bill is a 28% decrease.