On the first day in each month, Enid deposited $4 into her bank account and Jim deposited $3 into his. They opened these accounts on May 15, 1990. On December 31, 1990, they each had $72 dollars in their account. How much did each person deposit on May 15?
(Note: Neither person earned interest.)
Let X = amount Enid deposited on May 15.
and Y = amount Jim deposited on May 15.
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May 15 = X...........Y
June 1...4...........3
July 1...4...........3
Aug 1....4...........3
Sept 1...4...........3
Oct 1....4...........3
Nov 1....4...........3
Dec 1....4...........3
TOTAL...X+28.......Y+21
Each has 72 at the so
X+28=72
Y+21 = 72
Solve for X and Y.
Thank You!
Let's solve this step by step.
1. We know that Enid deposited $4 each month into her account, and Jim deposited $3 each month into his account.
2. They both opened their accounts on May 15, 1990.
3. We need to find out how many deposits they made from May to December in 1990. There are 8 months between May and December.
Enid: $4 x 8 months = $32
Jim: $3 x 8 months = $24
4. On December 31, 1990, they each had $72 in their account.
5. Let's subtract the deposits they made from the total balance on December 31 to find out each person's initial deposit.
Enid: $72 - $32 = $40
Jim: $72 - $24 = $48
Therefore, Enid deposited $40 on May 15, and Jim deposited $48 on May 15.
To find out how much each person deposited on May 15, we can start by calculating the total amount deposited by Enid and Jim from May to December.
Enid deposited $4 on the first day of each month, and there are 8 months from May to December (May, June, July, August, September, October, November, and December). So, the total amount Enid deposited in those 8 months is:
Enid's total deposit = $4 x 8 = $32
Similarly, Jim deposited $3 on the first day of each month, so we can calculate the total amount Jim deposited in those 8 months:
Jim's total deposit = $3 x 8 = $24
Now, we are given that both Enid and Jim had $72 in their accounts on December 31, 1990. Since they opened their accounts on May 15, it means that they each had the same amount in their accounts on that day.
So, we can subtract the total amount they both deposited from May to December ($32 + $24 = $56) from the total amount in their accounts on December 31 ($72). The result will give us the remaining amount that was in their accounts on May 15:
Remaining amount on May 15 = Total amount on December 31 - Total deposits from May to December
Remaining amount on May 15 = $72 - $56 = $16
Since Enid and Jim had the same amount on May 15, we divide the remaining amount by 2 to determine how much each person deposited on that day:
Amount deposited by each person on May 15 = Remaining amount on May 15 / 2
Amount deposited by each person on May 15 = $16 / 2 = $8
Therefore, both Enid and Jim deposited $8 on May 15, 1990.