Example 1
The Ferris wheel of the amusement park has 60 cabins, and it takes 20 minutes to turn around, 5 minutes after Xiao Wang enters the Ferris wheel cabin, Xiao Li also enters the Ferris wheel cabin, and then after () minutes, Xiao Wang and Xiao Li reach the same height.Solution:According to the "20-minute revolution", it can be seen that if a circle is 360°, then 5 minutes will rotate 360° 20 5=90°.a.2.5b.7.5
c.12.5
d.17.5
When Xiao Wang first entered the Ferris wheel cabin, it was at the lowest point of a circle.
5 minutes later, when Xiao Li entered the Ferris wheel cabin, Xiao Wang's Ferris wheel cabin turned 90 degrees.
If you want Xiao Wang and Xiao Li to reach the same height, you need the two of them to be on both sides of the highest point of the Ferris wheel, that is, to turn 90°+45°=135°, so you need 5+25=7.5 (minutes).
So, choose option B.
Example 2
A city plans to plant a kapok tree every 8 meters on both sides of a straight road, and hand over the tree planting task to two groups of workers A and B. If group B does the first 10 days, and the rest of the tasks are handed over to group A, then another 2 days will be completed. It is known that Group A has 5 more trees per day than Group B, so the road is () meters long.Solution:According to "Group A will do it for 3 days first, and Group A and B will cooperate for 4 days." Group B will be done for 10 days, and Group A will be completed in another 2 days. ", it can be seen that the column equivalence relation: 3 A + 4 (A + B) = 10 B + 2 A, simplified to obtain A B = 6 5.a.1224
b.1232
c.1240
d.1248
According to the "group A planted 5 trees per day compared with group B", it can be seen that group A planted (6-5) 5 6 = 30 trees per day, and group B planted (6-5) 5 5 = 25 trees per day.
A total of 25 10 + 30 2 = 310 (trees) need to be planted, and 310 2 = 155 (trees) need to be planted on each side.
If there is a 155-1 = 154 (space) interval on one side, then the road is 8 154 = 1232 meters long.
So, choose option B.
Example 3
The annual prices of "Reference News" and "Youth Digest" are 292 yuan and 156 yuan respectively. All the staff in the room subscribe to one of these two newspapers for 2,084 yuan, and if they subscribe to another variety, it costs 1,948 yuan, how many people are in the room?Solution:The number of people who subscribe to "Reference News" and "Youth Digest" is X and Y respectively.a.7b.9
c.11d.15
The equation can be listed from the meaning of the question: 292x+156y=2084, 156x+292y=1948. , which is simplified to obtain x+y=9.
So, choose option B.
Example 4
A cup of sugar water with a concentration of 50%, the concentration becomes 40% after adding a certain amount of water, and then after adding the same amount of water as the previous time, the sugar water becomes 60 grams, how many grams of sugar are in the sugar water?Solution:If there are x grams of sugar water with a concentration of 50%, the sugar in the sugar water is 50% x grams, and the amount of water added for the first time is y grams.a.18b.20
c.24d.30
According to "the concentration becomes 40% when a certain amount of water is added", the equation can be listed
To simplify, x=4y.
According to the equation "After adding the same amount of water as the previous time, the sugar water becomes 60 grams", the equation can be listed: x+2y=60.
Syntagion, solution x=40, y=10.
The sugar in the sugar water has 50% x = 50% 40 = 20.
So, choose option B.
Knowledge Points:
Solubility mass = solution mass concentration.
Concentration = solute mass Solution mass.
Example 5
In a given city, 60% of households subscribe to some kind of **, and 85% have a TV set. Assuming that these two events are independent, the probability that a family will be randomly selected and that the family will subscribe to both the ** and the TV is:Solution:According to "these two events are independent", the probability of subscribing to both this kind of ** and a TV set is 60% 85% 51%.a.0.09
b.0.25
c.0.36
d.0.51
So, choose option D.