Please see how to do this math problem below. Please list the formulas and explain the reasons.

Method 1 (enumeration method):

There are six combinations: 135, 153, 3 15, 35 1, 523, 53 1.

Method 2 (principle of distributed multiplication): There are three choices for one digit, two choices for ten digits, and 1 for hundred digits.

So * * * has: 3*2* 1=6 kinds.

2. solution: let the cost be x yuan.

According to the meaning of the question, the following formulas can be listed:

( 1+25%)*X*90%=4500

1.25*X=5000

X=400

So the cost price is 400 yuan.

3. Solution: If the length of the wall is x meters, the other side of the fence is (16/2-X) meters.

S = X * ( 16/2-X)

= 8X - X *X

= -(X -4) * (X -4) + 16

= 16 -[(X -4) * (X -4)]

When [(X -4) * (X -4)] =0, the maximum area s is 16.

That is, if and only if X=4, the maximum area is16m2.

4. Solution: 8 1 3 0

+ 3 1 8 1

= 1 1 3 1 1

First of all, we see that thousands of s+v equals two digits, so t can only be equal to 1. A can only be equal to 0.

Look at the ten digits again, then s+v can only be equal to 1 1. So the v in the hundredth place is 3.

So s equals 8.

Namely: a=0, t= 1, v=3, s=8.

5. Solution: a b c s

x 9

= s c b a

According to the vertical style, look at thousands first, and a * 9 can only wait for one digit, so A = 1.

Look at one more, so s=9.

Then look at the number on the hundred digits of the multiplicand. B*9 can only be a single digit, so B = 0 or 1.

If b = 1, then c can only be equal to 0, but this does not match the number, so it can only be b = 0.

So now, only consider that the decimal place of c*9+8 is 0(8 is a decimal place), that is, the decimal place of c*9 is 2. If you are familiar with the "99 multiplication table", it is not difficult to get it.

c=8。

Therefore, a= 1, b=0, c=8 and s=9.

I hope you can understand! !