Give some books to several students. If each student is given three books, then the remaining eight books. If each student in front gets five books, then the last student gets less than three. How many books are there? How many students are there?

Solution: Suppose there is a student.

According to the meaning of the question

3a+8-5(a- 1)& lt； 3( 1)

3a+8-5(a- 1)>0(2)

By (1)

3a+8-5a+5 & lt； three

2a & gt 10

A> v

By (2)

3a+8-5a+5 & gt； 0

2a & lt 13

a & lt6.5

Then the value range of a is 5.

Then a=6

There are 6 students, 3×6+8=26 books.

Tinplate can be made, each tinplate can be made into 25 boxes or 40 boxes, and two boxes in a box can be made into a set of cans. At present, there are 36 pieces of iron. How many tinplates does it take to make the box match the bottom of the box?

Analysis: Because there are always 36 iron boxes, x+y=36. Formula; The number of sheets made in the box+the number of sheets made at the bottom of the box = the total number of sheets made in cans * * * 36. The equation (1) is obtained. Because now a box body and two box bottoms are made into a set of cans, so; Number of boxes *2= number of box bottoms. This will make them equal. Equation (2)2* 16x=40y is obtained.

x+y=36 ( 1)

2* 16x=40y (2)

36-y=x (3) from ( 1)

Substituting (3) into (2) to obtain;

32(36-y)=40y

y= 16

If y= 16 is substituted (1), then x=20.

So; x=20

y= 16

Answer: Use 20 sheets as the box, and 16 as the bottom.

for reference only