7: Read the poem "A group of crows perched on a tree, there are countless crow trees. Three perched on a tree, five crows have no place to go. Five perched on a tree, one tree is free." Asking for crows and trees. How much each?
Solution: Suppose there are x trees
3x+5=5(x-1)
3x+5=5x-5
< p>5x-3x=5+52x=10
x=5
3×5+5=20
Answer: There are 20 crows and 5 trees
8: There are chickens and rabbits in the same cage. There are 35 heads on the top and 94 legs on the bottom. How many chickens and rabbits are there in each cage? There are 39 heads on top and 100 legs on bottom. How many chickens and rabbits are there?
1) Solution: Suppose there are x rabbits and 35-x chickens
4x+2(35-x)=94
4x+70-2x =94
2x=24
x=12
35-12=23
Answer: 23 chickens and 12 rabbits
2) Solution: Suppose there are x rabbits and 39-x chickens
4x+2(39-x)=100
4x+78-2x =100
2x=22
x=11
39-11=28
Answer: 28 chickens and 11 rabbits
9: Xiao Ming is 6 years old this year and his grandfather is 72 years old. How many years later will Xiao Ming be one-quarter of his grandfather's age?
Explanation: Suppose x years later, Xiao Ming’s age will be 1/4 of his grandfather
72+x=4(6+x)
72+x= 24+4x
4x-x=72-24
3x=48
x=16
Answer: After 16 years, Xiao Ming's age is 1/4 of his grandfather's age
10: the combined age of father and son is 40 years old.
Two years ago, the father's age was 8 times that of his son. How old are the fathers now?
Explanation: Suppose the father is x years old this year, then the son is 40-x years old this year
x-2=8(40-x-2)
x- 2=320-8x-16
8x+x=320-16+2
9x=306
x=34
40-34=6
Answer: The father is 34 years old and the son is 6 years old