Example 1
On the eve of the Mid-Autumn Festival, a store purchased a batch of mooncake gift boxes, and then sold more than 10 copies of half of the total number in the first week, and sold more than 5 copies of the remaining half in the second week.Solution:a.60b.80
c.100d.120
So, choose option D.
Example 2
A conference group rented more than 20 cars to pick up 2,220 participants from the hotel to the event site. The cart can send 50 people each time, the car can send 36 people each time, all vehicles send 2 times, and all vehicles are full, just after the delivery, the big car is better than the small car ().Solution:There are x large cars and y small cars.a.5 more.
b.2 more.
c.2 less.
d.5 cars less.
According to "more than 20 cars send 2220 people, and 2 full trips are just finished", the equation can be listed: 50 2x 36 2y 2220, simplified: 25x 18y 555.
According to the characteristics of the factor, it can be seen that 25x 18y 555 (x and y are positive integers), where 555 and 25x both contain the common factor 5, then 18y also contains the common factor 5, that is, 18y is divisible by 5, and y is an integer multiple of 5.
When y 5, 25x+18 5=555, the solution is x=186, x is not a positive integer, excluded;
When y 10, 25x+18 10=555, the solution is x15, which meets the condition that the total number of vehicles is more than 20.
So there are 15 more cars than cars 10 = 5 cars.
So, choose option A.
Knowledge Points:
The factor property is that in an indefinite equation, two of which contain a common factor (in this case, the factor is actually a divisor), the other term also contains a common factor. For example, in 3x+4y=15 (x and y are positive integers), where both 15 and 3x contain a common factor 3, then 4y also contains a common factor 3, then y is a multiple of 3; y can be equal to. When y=3, x=1, you can quickly solve the indefinite equation.
Example 3
Xiao Wang jumped from company A to company B, the total annual salary increased by 25%, the total salary of company B includes the cash part and the ** part, the ratio of total cash and ** total value is 3:1, and the ** value is calculated according to the *** price on the day of signing the contract. One year later, the company's stock price due to major changes is 48% higher than that of Xiao Wang's entry, if calculated according to the stock price at this time, Xiao Wang's actual total salary obtained by working in Company B for one year is compared with that in Company ASolution:The total salary of company A is 1200.a.10% decrease
b.A decrease of 15%.
c.An increase of 10%.
d.An increase of 15%.
According to the "25% increase in the total annual salary of Company B", it can be seen that the total salary of Company B is 1200 (1 25%) 1500.
According to "the ratio of total cash and total value of company B is 3:1", it can be seen that the total cash of company B is 1500 4 3 = 1125, and the total value of ** is 1500 4 1 = 375.
According to the "stock price ratio of 48% when Xiao Wang joined", it can be seen that the total value of ** is 375 (1 48%) 195.
Then the actual total salary of Company B is 1125 195 1320, 1320 1200, so Company B is actually more than Company A (1320 1200) 1200 10%.
So, choose option C.
Example 4
A gym has recently launched 4 courses A, B, C, and D, and each course has a consumption of 200 yuan, 300 yuan, 400 yuan, and 500 yuan respectively, and members can consume according to the balance in the recharge card. Member Xiao Li has 2,200 yuan left in his recharge card, and intends to consume at least 1 time for each course within the validity period, and the balance in the recharge card is just used up, so he is asked how many different possibilities are there for the combination of these 4 courses?Solution:According to the "consumption of at least 1 time for each course within the validity period", it can be seen that the total cost of 4 courses is 200 + 300 + 400 + 500 = 1400 (yuan), and there is 2200-1400 = 800 (yuan) left.a.3b.4
c.5d.6
According to "the balance is just used up", it can be seen that the 800 yuan can be combined as follows: 500 at a time + 300 at a time; 400 twice; 400 once + 200 twice; 300 twice + 200 once; Four times 200. There are 5 combinations in total.
So, choose option C.
Example 5
A product is available in small, medium, and large packaging sizes, with 10, 20, and 30 units per box. If the order quantity is an integer multiple of 10, the merchant randomly selects a shipment from all the FCL combinations where the total number of units is equal to the number of units ordered. If 70 of these items are known to be ordered in an order, the probability that the merchant will send out a shipment containing at least 1 large box is:Solution:From the total number of 70 pieces, divided into 10 boxes, 20 boxes, 30 boxes of specifications, the enumeration can obtain the following:a.62.5%
b.50%c.37.5%
d.25%
There are a total of 8 cases, and the first 4 are those that contain at least one large package, so probability = number of cases that meet the conditions Total number of cases = 4 8 = 50%.
So, choose option B.
Knowledge Points:
Probability = number of cases where the conditions are met Total number of cases.