花明月小升初数学难题(The math problem in the early stages)

2020年11月25日发(作者：赖名汤)

小升初数学难题（The math problem in the early stages）
A,

Several liters in brine, the first time to join salt accounted
for 8% of salt water after a certain amount of water, a second
time they join with the same amount of water for the first time,
the salt accounted for 5% of salt water, if the third time after
joining with the same amount of water for the first time, the
salt accounted for about a few percent of the salt water? (a
decimal before the percent)

(1) the first solution:

Examination site: concentration problem. Analysis: first after
adding water containing salt brine rate down to 8%, the second
time in as many salt rate dropped to 5% after water, it not
change the amount of sugar does not change, the quality of the
water, we may have to join the X originally some brine as 1,
then add water for the first time after the salt content is the
second time the (1 + X) X 8% salt content after adding water
is (1 + X + X) X 5%, so that we can work out how much water is
added X is, according to the meaning of the salt content and
add the same amount of water for the third time after salt
content. Answer: solution: set a cup of water to X,

After the first addition of x cup of water, the salt percentage
in brine changed to 8 % - that is, sugar (1 + x) * 8%,

The second time you add the same amount of water, the salt in
the salt water is a percentage of 5%, which is sugar (1 + x +
x) by 5%,



So you get 1 plus x times 8 is equal to 1 plus x plus x times
5%

X = 1.5,

For the third time, add the same amount of water, the salt of
salt water (1 + 1.5) by 8% (1 + 1.5 x 3) is approximately 0.036
= 3.6%,

So the amount of salt in the salt water after the third addition
of the same amount of water is 3.6%.

A: the third time after joining the same amount of water, then
the brine salinity is 3.6%. The review: this topic mainly
examines we should seize the salt is not a variable, because
of the added water, salt content would reduce, we may have to
join the water as x, the original brine as 1, joined by the first
and second water we can work out x, and x, we can directly into
the calculation for the third time after adding water salt
content.

(2) second solution:

Hold the salt in the salt water unchanged. 8% of the salt water
and salt: water = 8: (100-8) = 2 = they 40:46 0 5% of the salt
water and salt: water = 5:100-5) = 5 = 60 officers goes out water
increased by 760-760 = 460 (a) the third 300 add the same amount
of water, water with a total of 760 + 300 = 1060 (a) brine: 1060
+ 40 = 1100 (a) the third brine concentration after add the same
amount of water is: 40 members present 1100 = 3.6%



Second,

Three volumes of the same bottle are filled with an alcohol
solution, and alcohol and water are 2:1, 3:1, 4:1. What is the
ratio of alcohol to water when mixed with three bottles of
alcohol? (a)

A. 133:47 b.131:49

C. 33:12 d. 3:1

Answer: a,

Analytic: set the bottle volume is 1, because of alcohol and
water is 2:1, 3:1 and 4:1, so after three bottles of alcohol
solution blending, ratio of alcohol and water (2/3 + 3/4 + 4/5) :
(1/3 + 1/4 + 1/5) = 133:47

Three,

A concentration of 40% and 10% of the sugar water in the two
cups, together with a concentration of 30% sugar water; If you
add another 300 grams of sugar water, the concentration becomes
25%.

So how many grams of sugar water do you have?

(1) first solution:

300 * 20% = 60 (g), set X can be a total brine, 30% of brine


is heavy (X - 300), in accordance with the question to X - 60
= 25% to 30% (X - 300) solution to X = 600, 30% of the salt water:
X - 300 = 300-300 = 300 X 300 = 300 (g) 30% (g) : a concentration
of 40% saline X g, the concentration of 10% salt water (300 -)
X g, according to the question to 40% + 10% (300 -) X X X = 200
= 90 solution answer: 40% of the original 200 grams of salt
water.

N has a, b cups, a water, and a fruit juice. First pour the cup
of water into the cup and double the liquid in the cup. Pour
the cup of juice into a cup and double the liquid in the
cup. ...... If I pour four times, what is the concentration of
the two cups of juice?

Process:

The concentration of pure water is 0 % and the concentration
of pure juice is 100 %

The first one was 0%

B concentrations (100% + 0%) / 2 = 50%

The second nail concentration (50% + 0%) / 2 = 25%

B concentration 50%

The third dose is 25%

B concentrations (25% + 50%) / 2 = 37.5%



The fourth concentration (37.5% + 25%) / 2 = 31.25%

B concentration 37.5%

Because each time you pour a volume of solution from each
other's cup, the concentration of the new solution is the
average value of the concentration of the two solutions. So:
the first time: a: 0% b: 50% the second time: a: 25% b: 50% after
the third time; A: 25%, b: (50 + 25) / 2% = 37.5% and the fourth
time: a: (25 + 37.5) / 2% = 31.25% b: 37.5 %; a: 31.25%, b: (37.5
+ 31.25) / 2% = 34.375%, and the pure alcohol in the final second
glass is 34.375% of the alcohol solution

Four:

Has a reservoir containing 9 conduit, one of them as the inlet
pipe, the remaining eight root to the same outlet pipe. Inlet
pipe with uniform speed to the reservoir water flooding. Later
someone wants to open the outlet pipe, the water of the pool
all rows of light (at this moment has injected some water in
the pool). If the eight outlet pipe is opened entirely, need
3 hours to arrange all of the water in the pool light; If you
can only open 5 outlet pipes, you need 6 hours to drain all the
water in the tank.

(1) first solution:

Analysis: if you open a pipe that can drain portionper hour,
then 8 water pipes will drain 8 * 3 = 24 (portions) for 3 hours.
5 out of the water pipe for 6 hours total discharge 5 * 6 = 30
(part); In two cases, the water intake in three hours is 30-24


= 6 (part). The intake of water per hour is 6 and 3 = 2 (part).
In 4.5 hours, the original water in the pool and the water in
the water inlet are 8 * 3 + (4.5-3) * 2 = 27 (part).

Solution: to open a water pipe that can discharge
per hour, 8 outlet pipes will be drained for 3 hours, 8 * 3 =
24 (part); 5 out of the water pipe for 6 hours total discharge
5 x 6 = 30 (part).

30-24 = 6 (part), these six are the water in the = 3hours.

(30-24) to sign (6-3) = 6 to 3 = 2 (part), this is the inlet
water per hour.

[8 x 3 + (4.5-3) x 2

24 + 1.5 x = [2] present 4.5

27 members present = 4.5

= 6 (root)

Answer: it is necessary to open 6 water pipes at the same time.
The key is to open a pipe and drain

Five:

The exhibition opened at 9 o 'clock, but there were long queues
for admission. From the first audience, the number of
spectators per minute is the same. If there are three entrance
openings, there will be no queue at 9:9. If there are five


entrance openings, there will be no queue at 9:5. So what time
does the first audience arrive?

(1) first solution:

Solution: the number of people who pass by one minute is one.
The speed of people's arrival: (3 x 9-5 x 5) is the number of
people who are waiting for: 3 times 9-0.5 times 9 = 22.5. These
people are accumulating at the rate of 0.5 per minute, so the
previous queue is 22.5 = 45 minutes, which means that the first
audience arrives at 8:15.

Knowledge summary

(1) the phalanx problem

Number of outer edges - 2 = the number of inner sides

(number of outer edges - 1) x 4 = outer perimeter

Number of outer edges - 2 - hollow side length 2 = real area

The train overpasses

The length of the car + the bridge = speed * time

The length of the car and the length of the car

The length of the length of the car is the speed difference

The encounter and problem of the train with the driver on the