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.