Admission price per person: 13 yuan 1 1 Yuan 9 yuan.
1. There are two tour groups today, and the tickets for the two groups are 13 14 yuan; If you buy tickets together, you need to pay 1008 yuan. How many people are there in each of these two tour groups?
Solution:
1008 can only be divisible by 9,1008/9 =112.
Make the two tour groups each have x people, namely 1 12-x people.
Then there is
13x+ 1 1( 1 12-x)= 13 14
=》x = 4 1 1 12-x = 7 1
=> The two tour groups are 4 1 person and 7 1 person respectively.
2。 A shop needs to buy a batch of TV sets and washing machines. According to the survey, TV sets are not less than half of washing machines. The buying and selling prices of these two kinds of electrical appliances are as follows.
Classified TV washing machine
Purchase price (RMB/set) 1800 1500
Price (RMB/set) 2000 1600
It is planned to purchase 65,438+000 sets, and the maximum fund raised is 65,438+0,665,438+0, 800 yuan.
(1) Calculate how many purchase schemes there are (excluding other expenses).
(2) Find the most profitable scheme.
Solution:
A shop needs to buy a batch of TV sets and washing machines. According to the survey, TV sets are not less than half of washing machines. The buying and selling prices of these two kinds of electrical appliances are as follows.
Classified TV washing machine
Purchase price (RMB/set) 1800 1500
Price (RMB/set) 2000 1600
It is planned to purchase 65,438+000 sets, and the maximum fund raised is 65,438+0,665,438+0, 800 yuan.
(1) Calculate how many purchase schemes there are (excluding other expenses).
Solution: Buy X TV sets and buy (100-x) washing machines.
Judging from the meaning of the question:
x≥ 1/2( 100-x)
1800 x+ 1500( 100-x)≤ 16 1800
Solution:
100/3≤x≤ 1 18/3
Because x is an integer,
So x = 34, 35, 36, 37, 38, 39.
Then 100-x = 66, 65, 64, 63, 62, 6 1
Answer: You can buy 34 TV sets and 66 washing machines.
Bought 35 TV sets and 65 washing machines.
Bought 36 TV sets and 64 washing machines.
Bought 37 TV sets and 63 washing machines.
I bought 38 TV sets and 62 washing machines.
Buy 39 TV sets and 6 1 washing machine.
(2) Find the most profitable scheme.
Because in 2000 >; 1600,
So you should buy as many TV sets as possible.
You should buy 39 TV sets and 6 1 washing machine.
Profit: 39× 2000+6/kloc-0 /×1600 =175600 (yuan)
Answer: you should buy 39 TV sets, 6 1 washing machine, and the profit is 175600 yuan.
3。 For any two numbers x and y, define a new "*", x * y = ax+by+c.
Solution:
3*5=3A+5B+C= 15
4*7=4A+7B+C=28
Subtract A+2B= 13.
A= 13-2B replaces 3A+5B+C= 15.
39-6B+5B+C= 15
C-B=-24
Add a +2B= 13.
A+B+C=- 1 1
1 * 1 = A+B+C =- 1 1