Bank transactions and Algebra

by Grace
(Philippines)

APC bank charges 11 dollars for ATM users who are account holders of local banks. It charges 26 dollars for account holders of international bank. After a day the bank was able to collect 1185 dollars from one of their ATMs. There were 10 transactions more made by an international bank account holder compared with those by local bank account holders. How many ATM transactions were made on that particular day? How many transactions were made by international bank account holders? By local bank account holders?

Solution

Let x be the number of transactions made by account holders of local banks.

Let y be the number of transactions made by account holders of international banks.

Money collected from account holders of local bank = 11x

Money collected from account holders of international bank = 26y

The number of transactions made by account holders of international banks is 10 more than the number of transactions made by account holders of local banks.

In other words, y = x + 10

Money collected from account holders of local bank plus money collect from account holders of international banks equal 1185 dollars.

11x + 26y = 1185 (1)

y = x + 10 (2)

Substitute x + 10 for y in (1)

11x + 26 (x + 10) = 1185

11x + 26x + 260 = 1185

37x + 260 = 1185

37x = 1185 - 260

37x = 925

x = 925/37

x = 25

y = x + 10 = 25 + 10 = 35

On that day, there were 60 ATM transactions

The number of transactions made by account holders of local banks is 25.

The number of transactions made by account holders of international banks is 35.