# Math Help - help with a maths please

1. ## help with a maths please

it is a maths question for students aged around 14 in my country. I am shamed that I don't know how to solve it

The question is something like:

Person A has a sum of money on Monday, and he spent $10 EACH day, and then he will save HALF of the money left on that day. After he spent$10 on Friday, he had no more money left. So how much did he orginially have on Monday?

At first I don't quite understand the question, but here I hope to clarify something that, Person A spent $10 FIRST on each day, then there will be some money left, then he will save half of the money left, and the rest of the money (not saved or spent) will be counted as the starting point of money for the next day. 2. Originally Posted by kenny1999 it is a maths question for students aged around 14 in my country. I am shamed that I don't know how to solve it The question is something like: Person A has a sum of money on Monday, and he spent$10 EACH day, and then he will save HALF of the money left on that day. After he spent $10 on Friday, he had no more money left. So how much did he orginially have on Monday? At first I don't quite understand the question, but here I hope to clarify something that, Person A spent$10 FIRST on each day, then there will be some money left, then he will save half of the money left, and the rest of the money (not saved or spent) will be counted as the starting point of money for the next day.
If you have $\x_n$ at the start day $n$ you have $x_{n+1}=(x_n-10)/2$ dollars at the start of the next day.

Reversing this we get:

$x_n=2 x_{n+1}+10$

Now Friday is day $5$ and Monday is day $1$, and you are told that $x_5=10$

CB

3. If we work backwards

After spending $10 on friday he had$0 money left

therefore before halving his money on thursday he had $20 left. This meant he spent$10 to get to his total of $20 which meant at start of day he had$30

therefore before halving his money on wednesday he had $60 left. This meant he spent$10 to get to his total of $60 which meant at start of day he had$70

therefore before halving his money on tuesday he had $140 left. This meant he spent$10 to get to his total of $140 which meant at start of day he had$150.

therefore before halving his money on monday he had $300 left. This meant he spent$10 to get to his total of $300 which meant at start of day he had$310.

lets check
Monday 310 spent 10 leaves 300 save half to leave 150
Tuesday 150 spent 10 leaves 140 save half to leave 70
Wednesday 70 spent 10 leaves 60 save half to leave 30
Thirsday 30 spent 10 leaves 20 save half to leave 10
Friday 10 spent 10 to leave 0

4. Yet a third way to do this (akin to Captain Black's way):

Suppose he starts with x dollars. Monday he spends $10, leaving x-10. Then he saves 1/2 of that, 1/2(x-10)= x/2- 5, so he has x-10- (x/2- 5)= x- 10- x/2+ 5= x/2- 5 left. Tuesday he spends$10, leaving x/2- 15 and saves 1/2 of that, x/4- 15/2, so he has x/2- 15- (x/4- 15/2)= x/4- 15/2.

Wednesday he spends $10, leaving x/4- 35/2 and saves 1/2 of that, x/8- 35/4 so he has x/4- 35/2- (x/8- 35/4)= x/8- 35/4. (You should be able to see a pattern here.) Thursday he spends$10, leaving x/8- 75/4 and saves 1/2 of that, x/16- 75/8 so he has (x/8- 75/4)- (x/16- 75/8)= x/16- 75/8.

Finally, on Friday he spends \$10, leaving x/16- 155/8= 0.

Solve that equation for x.

5. hmnnn . . .

x/16- 155/8= 0

x/16 = 155/8

x = 16(155)/8

x = 2(155)

x = 310