Eddie has $450 in her savings account she deposit $40 each month one has 975 in his checking account he writes a check for 45. $45 each month for his cell phone bill he also writes a check for 19. $55 each month for his water bill after how many months with eddie and phone have the same amount of money in their accounts?

After 5 months both Eddie and Phone have the same amount of money in their accounts

Solution:

Given, Eddie has $450 in her savings account she deposit $40 each month  Then, series of Eddie account balance is 450, 450 + 40, 450 + 40 + 40 ………….

⇒ 450, 490, 530, ……..  

This is an Arithmetic progression with first term a = 450 and common difference d = 40.

Now, phone has 975 in his checking account he writes a check for $45 each month for his cell phone bill  

He also writes a check for $20 each month for his water bill  

Then, in total he draws 45 + 20 = 65 every month.

So, series of phone account balance will be 975, 975 – 65, 975 – 65 – 65. ………..

⇒ 975, 915, 850, ………… this is an A.P with first term a = 975 and common difference d = - 65

We have to find after how many months with Eddie and Phone have the same amount of money in their accounts?

Now nth term of Eddie series must be equal to nth term of phone series where n is our required number.

Then, nth term of Eddie = nth term of phone  

In A.P nth term = a + (n - 1)d

450 + (n – 1)40 = 975 + (n – 1)(-65)  

(n – 1)40 – (n – 1)(-65) = 975 – 450

(n – 1)(40 + 65) = 525

(n – 1)(105) = 525

n - 1 = 5

n = 6

Hence, at 6th term which means after(6 – 1) = 5  months, both accounts will have same amount.