How does this "basic" card trick work I am a bit confused on how the attached cardtrick works, if anyone can explain that would be amazing, thanks! (im in 7th grade btw so its probably simple to most of you)
Step 1
Remove all face cards and the tens cards from a standard deck of playing cards.
You will not need these cards for the trick. Check that you have 36 cards left.
Step 2
Have an audience member select any of the 36 cards at random without showing
you the card.
Step 3
Ask the audience member to follow these directions using the number from the
card. (An ace counts as 1.)
 Multiply the number by 5.
 Add 6 to the product.
 Multiply the sum by 2.
Step 4
Have the audience member choose a second card at random without showing you
the card. Ask the person to add the number from this card to the result from Step
3, and then reveal the total to you.
Step 5
Mentally subtract 12 from the total. The difference will be a two-digit number. The
two digits will be the two numbers on the cards the audience member selected.
Step 6
“Magically” reveal these two numbers to the audience member.
 A: The numbers on the cards are between 1 and 9, so let's say that the two numbers are $x$ and $y$, both between 1 and 9. 
You compute (from the rules)
$$
5x\\
5x + 6\\
2(5x + 6) = 10x + 12
$$
Now you add $y$ to that to get
$$
10x + y + 12
$$
and then you subtract 12 to get
$$
10x + y
$$
Notice that the tens digit of this number is $x$ (the value on the first card) and the 1s digit is $y$ (the value on the second card). So it works!
A: Let n be the number on the first card.
Multiply by 5 --> 5n
Add 6 --> 5n + 6
Multiply sum by 2 --> 2(5n + 6) = 10n + 12
Let s = number on second card
Add number on second card to previous sum --> 10n + 12 + s
Subtract 12 --> 10n + 12 + s - 12 = 10n + s
Now since you cleared the deck of higher value cards, the numbers you have are single-digit integers. 
If you had for example n = 5 and s = 3, 10n + s = 53
The tens digit is 10n so n = tens digit = 5
The units digit is s so s = units digit = 3
Looks pretty stupid when you lay it out this way, doesn't it? Yet it is easy to fool people of weak minds (check Star Wars )
All these guess a number 1 to 10 tricks work the same way. There are many others including games with people's ages, date of birth, etc. If you multiply by 100 instead of 10 (here you did 5 times 2 for the 10, disguised) you can do two-digit numbers. Sometimes you do the last subtraction yourself to amaze them even more.
Have fun.
