mike and kate plan to save money for their wedding over a 20 - month period. they will need to save $8,000…

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 theyve 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 theyve 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. please select the best answer from the choices provided

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 theyve 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 theyve 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. please select the best answer from the choices provided

Answer

Explanation:

Step1: Calculate the original monthly - saving amount

They saved $4000 in 12 months. The original monthly - saving amount $m=\frac{4000}{12}=\frac{1000}{3}$ dollars.

Step2: Analyze Option A

The original plan was for 20 months, and now they postpone the wedding by 2 months, so the new time period is $20 + 2=22$ months. They have already saved $4000$ in 12 months. The remaining time is $22−12 = 10$ months. The amount they will save in the remaining 10 months at the original rate is $10\times\frac{1000}{3}=\frac{10000}{3}\approx3333.33$ dollars. The total amount they will save is $4000+\frac{10000}{3}=\frac{12000 + 10000}{3}=\frac{22000}{3}\approx7333.33<8000$ dollars.

Step3: Analyze Option B

The original monthly - saving amount is $\frac{1000}{3}$ dollars. They increase the monthly - saving amount by $80$ dollars. The remaining time is $20 - 12=8$ months. The new monthly - saving amount is $\frac{1000}{3}+80=\frac{1000 + 240}{3}=\frac{1240}{3}$ dollars. The amount they will save in the remaining 8 months is $8\times\frac{1240}{3}=\frac{9920}{3}\approx3306.67$ dollars. The total amount they will save is $4000+\frac{9920}{3}=\frac{12000+9920}{3}=\frac{21920}{3}\approx7306.67<8000$ dollars.

Answer:

d. Neither option A nor option B will allow them to meet their goal.