Math Problems loads of ppl get wrong

I go to a Tea Shop.
I buy 1 tea and 1 biscuit.
It costs £1.10 ( pound sterling )
The Tea costs exactly £1 more than the biscuit.
How much was the biscuit, and how much was the tea ?

Q2 )

In a lake, the amount of fish doubles each day, the lake is filled up on the 48th day. How many days would it take to fill up half of the lake ?

A1) The tea costs £1.05, the biscuit costs £0.05.

People usually use their system 1 (en.wikipedia.org/wiki/Thinking,_Fast_and_Slow#Two_systems) to answer this one quickly (and incorrectly), initially thinking it would be £1 for the tea and £0.10 for the biscuit.

A2) 47 days.

Again, system 1 is at play, when people who are not familiar with exponential growth from their own experience think that half the fish must mean half of the time (which would be correct for linear growth, but is incorrect for exponential growth)

Well done @Thalassokrator, yes it is that system...

#1

Biscuit 1.10
Tea 2.10

And it’s not a math problem but reading carefully

I remember the two problems and found where I first saw them: youtu.be/OZal6R895VM

umm im in 5th grade am i supposed to know that?

You can figure it out @hicham_habboub

Think of it this way.

An apple and an orange cost a dollar and ten cents.

Apples cost a dollar more than oranges.

That means you could save a dollar by buying an orange rather than an apple. That means two oranges cost ten cents.

That means an orange costs a nickel.

If you find it difficult it's because nobody has explained to you how to solve problems like this.

@hicham_habboub
Depends. The first one is certainly doable for a normal fifth grader, even though you might not yet be familiar with algebra (you don't really need it when the puzzle is so easy).
You can do it with basic logic. But your brain is usually lazy and doesn't want to use logic.

Intuition might tell you that the biscuit is £0.10, but giving it some thought you'll see that it can't be, because then the tea would be £1.10 and together they'd be £1.20, which is clearly more than £1.10.

So the biscuit must be cheaper than £0.10. You can either find the price by trial and error or you can reason that after you subtract the £1 (the price difference between the two items) from the total price of £1.10, both items must share the remaining £0.10 equally. If they didn't the price difference between them wouldn't be £1, would it? It would be £1 PLUS the extra difference of the unequally shared £0.10.
So you get the correct answer by dividing £0.10 by two to obtain £0.05 for the biscuit and £0.05 extra (!) to be added to the price difference (that was already £1), giving a total price of £1.05 for the tea.

Edit: StingerPuzzles beat me to it and actually provided an explanation that I find easier to follow than my own.

@hicham_habboub
The first one involves basic algebra that was taught to me in 5th grade in school.
So, if you know algebra you should know it as you can simply form a linear equation based on the parameters.

The second one is logical and can be solved in mind. In case of mathematical explanation, it's an exponential growth so you need to know about exponents. I read them in 7th grade in school. It doesn't matter if you don't know mathematically but it would be good if you know it logically.

Simply form a linear equation based on the Parameters🧐

vs

split the diff💁