Question

The ratio of money in Terry's bank account to Faye's bank account was 3:5.

Terry then put £220 in his account and Faye withdrew £300 from her account.
They now had the same amount in their accounts.
How much did Terry initially have?

Answer 1

Terry had £780 initially and Faye had £1300

Explanation:

System of Equations

We'll call the following variables:

x = Terry's balance in his bank account

y = Faye's balance in her bank account

The initial relation between them is:

`(x)/(y)=(3)/(5)`

Cross-multiplying:

5x = 3y [1]

If Terry put £220 in his account he had x+220 and if Faye withdrew £300 from her account, she had y-300. Both quantities are equal, thus

x + 220 = y - 300

Subtracting 220:

x = y - 520 [2]

Substituting in [1]

5(y - 520) = 3y

Multiplying:

5y - 2600 = 3y

Adding 2600 and subtracting 3y:

2y = 2600

Dividing by 2:

y = 1300

From [2]:

x = 1300 - 520

x = 780

Terry had £780 initially and Faye had £1300