Mike and Kate plan to save money for their wedding over a 20 month period. They will need to save \( \$ 8,000 \) to help pay for the wedding. They set aside the same amount each month. After a year they saved \( \$ 4,000 \). Mike and Kate know they must adjust their plan in order to meet their goal, so they came up with the following options: Option A: Stay with saving the same amount they ve been saving each month but postpone the wedding 2 months. Option B: Increase the amount of money they save each month by \( \$ 80 \) from what they've been saving. Which of the following is a true statement? a. Only option A will allow them to meet their goal. b. Only option B will allow them to meet their goal. c. Saving by either option A or option B will allow them to meet their goal. d. Neither option A nor option B will allow them to meet their goal.

To determine which option will allow Mike and Kate to meet their goal of saving \( \$ 8,000 \) for their wedding, we need to analyze both options based on their current savings plan. ### Known Conditions: - Total savings goal: \( \$ 8,000 \) - Total saving period: 20 months - Amount saved after 12 months: \( \$ 4,000 \) - Monthly savings so far: \( \frac{4000}{12} = \frac{1000}{3} \approx 333.33 \) ### Step 1: Calculate Current Monthly Savings Let \( x \) be the amount they save each month. After 12 months, they have saved \( 12x = 4000 \). Thus, we can find \( x \): \[ x = \frac{4000}{12} = \frac{1000}{3} \approx 333.33 \] ### Step 2: Calculate Total Savings in 20 Months If they continue saving the same amount for the remaining 8 months, their total savings will be: \[ \text{Total savings} = 20x = 20 \times \frac{1000}{3} = \frac{20000}{3} \approx 6666.67 \] ### Step 3: Analyze Option A **Option A:** Postpone the wedding by 2 months, making the total saving period 22 months. In this case, the total savings will be: \[ \text{Total savings} = 22x = 22 \times \frac{1000}{3} = \frac{22000}{3} \approx 7333.33 \] ### Step 4: Analyze Option B **Option B:** Increase the monthly savings by \( \$ 80 \). New monthly savings will be: \[ x + 80 = \frac{1000}{3} + 80 = \frac{1000}{3} + \frac{240}{3} = \frac{1240}{3} \approx 413.33 \] Total savings over 20 months with the increased amount: \[ \text{Total savings} = 20 \left( \frac{1240}{3} \right) = \frac{24800}{3} \approx 8266.67 \] ### Step 5: Compare Total Savings to Goal - **Total savings with Option A (22 months):** \( \approx 7333.33 \) (not enough) - **Total savings with Option B (20 months):** \( \approx 8266.67 \) (sufficient) ### Conclusion - **Option A** will not allow them to meet their goal. - **Option B** will allow them to meet their goal. Thus, the correct answer is: **b. Only option B will allow them to meet their goal.**