What is the fraction

Question

 Koos spent 3/7 of his monthly pocket money during the first week. the following week he spends two-thirds of what he spent the previous week. The fraction of the pocket money that is still left

Answer 1

Let x be the amount Koos has in pocket money.

We are told that Koos spends 3/7 of that amount in the first week. That can be stated as Spent = (3/7)x.

The money Koos has left is(1 - 3/7)x. This can be simplified to (4/7)x.

Thwen we learn that Koos spent (2/3) of the smount he spent the first week. That can be written as:

Second Week Spend = (2/3)(3/7)x [ Spent 2/3 of the first week's spend of (3/7)x.]

Koos starts with x. Subtract the first and second week's spending to determine the amount Koos has left:

Money Left = x - (3/7)x - (2/3)(3/7)x

Money Left = x - (3/7)x - (6/21))x

Money Left = x - (7/7)(3/7)x - (6/21))x

Money Left = x - (21/49)x - (6/21))x

Money Left = x - (21/49)x - (6/21))x

Money Left = x - (3/7)x - (6/21))x

Money Left = (1/7)x

Answer 2

Let's say Koos had 1 dollar at the start of the month. Any fraction they take out or spend will be cents spent.

So we need to find how much was spend in each week

Week 1 Koos spent = 3/7

In week 2 spend = two-thirds of what he spent the previous week = 2/3*3/7 = 6/21 = 2/7

Total spending for 2 weeks = 3/7+2/7 = 5/7

Balance will be = 1 - 5/7 = 2/7

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