When 1570 was divided by the integer of 3 digit, remainder was 23.
Find the least integer among such integers.
Find the least integer among such integers.
Showing posts with label KOC. Show all posts
Showing posts with label KOC. Show all posts
Math Problem : C.31 Exchange rate of Pound and Won
The unit of British money is pound and the unit of South Korean money is won.
When 1 pound = 180 yen and 1 won = 0.11 yen, how much is 77 pounds in won?
When 1 pound = 180 yen and 1 won = 0.11 yen, how much is 77 pounds in won?
Math Problem : C.30 Calculation of measure of time
How many times of 1 hour and 20 minutes and 24 seconds is 3 hours and 54 seconds?
Math Problem : C.27 Concentration of salt solution after operation
Salt solution 100g is taken out of 1000g of salt solution with 10% concentration and 100g of water is added to the remaining salt solution.
After stirring well, the salt solution 200g is taken out and 200g of water is added.
Find the concentration of the salt solution at this time.
After stirring well, the salt solution 200g is taken out and 200g of water is added.
Find the concentration of the salt solution at this time.
Math Problem : JJ.54 Another partition of regular hexagon
As shown in the figure, a regular hexagon with all sides 6cm is divided into two portions by the straight line.
Find the ratio of the area of the portion of X and Y by the ratio of the least integer.
Find the ratio of the area of the portion of X and Y by the ratio of the least integer.
Math Problem : GGG.6 Quotient is rounded off at 1st decimal place
Division process is carried out and quotient is to be calculated to the 1st decimal place and rounds off the 1st decimal place.
Two calculation was made, one calculation was rounded off the 1st decimal place of the quotient when a certain integer of double digit was divided by 7 and another calculation was rounded off the 1st decimal place of the quotient when it was divided by 8.
Answer the following questions.
(1) Find the largest number in such integers of double digit.
(2) Find all the number of such integers of double digit.
Two calculation was made, one calculation was rounded off the 1st decimal place of the quotient when a certain integer of double digit was divided by 7 and another calculation was rounded off the 1st decimal place of the quotient when it was divided by 8.
Answer the following questions.
(1) Find the largest number in such integers of double digit.
(2) Find all the number of such integers of double digit.
GG.34 Multiple of each number of digit
According to the following example, the number of all digits of a certain integer is multiplied and this operation is repeated until the answer becomes the number of single digit.
Answer the following questions.
Answer the following questions.
<Example>
327 → 3 × 2 × 7 = 42 → 4 × 2 = 8
73 → 7 × 3 = 21 → 2 × 1 = 2
(1) Find the final answer when 279 is operated.
(2) Find the number of the integer of double digit when it is operated, the final answer becomes 6.
327 → 3 × 2 × 7 = 42 → 4 × 2 = 8
73 → 7 × 3 = 21 → 2 × 1 = 2
(1) Find the final answer when 279 is operated.
(2) Find the number of the integer of double digit when it is operated, the final answer becomes 6.
CC.12 Discounted ticket price
The price for the ticket from A station to B station is 2000 yen.
By the coupon ticket of a six-sheet set, it becomes 18% discount and by the coupon ticket of a ten-sheet set, it becomes 20% discount.
You buy tickets for 48 persons combining these tickets or coupon tickets.
When you buy them by the cheapest combination, find the price per person.
By the coupon ticket of a six-sheet set, it becomes 18% discount and by the coupon ticket of a ten-sheet set, it becomes 20% discount.
You buy tickets for 48 persons combining these tickets or coupon tickets.
When you buy them by the cheapest combination, find the price per person.
A.2 2/3 of 5 hours and 15 minutes
How many hours and how many minutes are 2/3 of 5 hours and 15 minutes?
J.23 Length in rectangle
There is a rectangle as shown in the figure.
AB = 3.5 cm, AD = 8.4 cm, BD = 9.1 cm.
AE is vertical to BD.
Find the length of AE at this time.
A.5 Magic square 3 x 3 (2)
Other numbers are put into the remaining grids and it is arranged that products of three numbers in any vertical or horizontal row become same.
Find the number in A at this time.
EE.7 Length of a candle
There is a candle which is becoming short at a fixed rate when setting fire to the candle.
I was going to investigate in how many minutes it would be burned out when fire is set to this candle.
Since I wanted to go to a toilet suddenly 6 minutes after beginning observation, I extinguished fire once and went to a toilet.
Then, after returning from the toilet, I set fire once again 5 minutes after extinguishing fire exactly and I continued observation.
The change of the length of the candle became as the graph.
Answer the following questions.
(1) Find the length of the candle 21 minutes after setting fire first.
(2) Find the time when the length of the candle becomes 3 cm after setting fire first.
I was going to investigate in how many minutes it would be burned out when fire is set to this candle.
Since I wanted to go to a toilet suddenly 6 minutes after beginning observation, I extinguished fire once and went to a toilet.
Then, after returning from the toilet, I set fire once again 5 minutes after extinguishing fire exactly and I continued observation.
The change of the length of the candle became as the graph.
Answer the following questions.
(1) Find the length of the candle 21 minutes after setting fire first.
(2) Find the time when the length of the candle becomes 3 cm after setting fire first.
EE.6 Travel distance and railway fare
Table 1 expresses the travel distance between the stations of a certain railroad.
Moreover, the relation between the travel distance of this railroad and a fare is shown as Fig. 1.
In the graph of Fig. 1, the point indicated by ○ is not included in a graph the point indicated by ● is included in the graph.
Moreover, the relation between the travel distance of this railroad and a fare is shown as Fig. 1.
In the graph of Fig. 1, the point indicated by ○ is not included in a graph the point indicated by ● is included in the graph.
For example, the travel distance from B station to C station is 185.8 km and the fare is 3810 yen.
The travel distance from B station to D station is 240 km and the fare is 4430 yen.
Even when travel distance exceeds 260 km, the rule of the fare of Fig. 1 is applied.
Answer the following questions.
(1) Find the travel distance from A station to D station.
(2) After Taro got on from A station to B station and finished shopping, he got on from B station to D station.
Jiro got on from A station to D station without stopping over.
How much was the sum total of the fare which Taro paid more than the fare which Jiro paid?
The travel distance from B station to D station is 240 km and the fare is 4430 yen.
Even when travel distance exceeds 260 km, the rule of the fare of Fig. 1 is applied.
Answer the following questions.
(1) Find the travel distance from A station to D station.
(2) After Taro got on from A station to B station and finished shopping, he got on from B station to D station.
Jiro got on from A station to D station without stopping over.
How much was the sum total of the fare which Taro paid more than the fare which Jiro paid?
EE.4 Partition in a water tank
As shown in Fig. 1, the tank of a rectangular prism is divided into X and Y by partition of a rectangle.
Water is poured into X and Y from the water pipes A and B respectively at the same time at a fixed rate.
The graph of Fig. 2 shows the relation of the height of each water surface of X and Y and the time from the start of pouring water.
The thickness of the wall of a tank and a partition is not considered.
Answer to the following questions.
(1) Find the volume of the water which is poured out in one minute from the water pipe A.
(2) Find all the time from the start of pouring water when the difference of the height of the water surface of X and Y becomes 4 cm.
(3) Find the time from the start of pouring water when the tank is filled with water.
Water is poured into X and Y from the water pipes A and B respectively at the same time at a fixed rate.
The graph of Fig. 2 shows the relation of the height of each water surface of X and Y and the time from the start of pouring water.
The thickness of the wall of a tank and a partition is not considered.
Answer to the following questions.
(1) Find the volume of the water which is poured out in one minute from the water pipe A.
(2) Find all the time from the start of pouring water when the difference of the height of the water surface of X and Y becomes 4 cm.
(3) Find the time from the start of pouring water when the tank is filled with water.
EE.3 One water feeding pipe and two draining pipes
Fig. 1 shows a vessel of the square pillar whose area of the bottom is 300 cm2 and depth is 50 cm.
Water pours in from A pipe and water comes out from B pipe and C pipe.
The graph of Fig. 2 expresses the relation of the depth of water and time.
Answer the following questions.
(1) Water is poured in from A pipe for the first 5 minutes with closing B pipe and C pipe.
Find the amount of the water poured per minute from A pipe.
(2) A pipe and C pipe were closed for the following 6 minutes and water was poured out from B pipe.
Furthermore, B pipe was closed for the following 3 minutes and water was poured in from A pipe and poured out from C pipe.
After that, all three pipes are opened.
Then find the time from the start when a vessel is filled with water.
Water pours in from A pipe and water comes out from B pipe and C pipe.
The graph of Fig. 2 expresses the relation of the depth of water and time.
Answer the following questions.
(1) Water is poured in from A pipe for the first 5 minutes with closing B pipe and C pipe.
Find the amount of the water poured per minute from A pipe.
(2) A pipe and C pipe were closed for the following 6 minutes and water was poured out from B pipe.
Furthermore, B pipe was closed for the following 3 minutes and water was poured in from A pipe and poured out from C pipe.
After that, all three pipes are opened.
Then find the time from the start when a vessel is filled with water.
DD.46 Four animals on a rectangle
As shown in the figure, a monkey, a dog, a cat, and a mouse are in each vertex of the rectangle of 4 m long and 8 m wide.
Now, they began to turn around on the side of the rectangle counterclockwise at the same time.
Each speed is that a monkey is at 80 cm/s, a dog is at 60 cm/s, a cat is at 50 cm/s, a rat is at 30 cm/s.
Answer the following questions.
(1) Find the time when four animals pass along the same place at the same time for the first time.
(2) Find the time to come to the vertex at the same time for the first time where each animal is there at first.
Now, they began to turn around on the side of the rectangle counterclockwise at the same time.
Each speed is that a monkey is at 80 cm/s, a dog is at 60 cm/s, a cat is at 50 cm/s, a rat is at 30 cm/s.
Answer the following questions.
(1) Find the time when four animals pass along the same place at the same time for the first time.
(2) Find the time to come to the vertex at the same time for the first time where each animal is there at first.
I.19 What day of the month
January 1, 2008 of the leap year was Tuesday.
What day is it the last Tuesday of January, 2010?
What day is it the last Tuesday of January, 2010?
DD.45 Carry an iron plate
As shown in the figure, cylinders with same form and same size are rolled without sliding so that they may carry an iron plate in the direction of an arrow.
A radius at the bottom of each cylinder is 15 cm and each cylinder rolls with a fixed speed and it is rotated one time in 12 seconds.
An iron plate moves without sliding on a cylinder.
The cylinder is placed so that it may not contact mutually, even when it rolls.
Answer the following questions.
Pi is assumed to be 3.14.
(1) Find the length where the cylinder moves rolling in the direction of an arrow in one second .
(2) Find the distance where an iron plate moves in the direction of an arrow in 10 seconds.
A radius at the bottom of each cylinder is 15 cm and each cylinder rolls with a fixed speed and it is rotated one time in 12 seconds.
An iron plate moves without sliding on a cylinder.
The cylinder is placed so that it may not contact mutually, even when it rolls.
Answer the following questions.
Pi is assumed to be 3.14.
(1) Find the length where the cylinder moves rolling in the direction of an arrow in one second .
(2) Find the distance where an iron plate moves in the direction of an arrow in 10 seconds.
D.26 Speed ratio of two persons
While Taro walks seven steps, Jiro walks five steps.
Moreover, Jiro walks by 11 steps along the distance where Taro walks by ten steps.
Find the ratio of the speed Taro and Jiro walk by the ratio of the least integer.
Moreover, Jiro walks by 11 steps along the distance where Taro walks by ten steps.
Find the ratio of the speed Taro and Jiro walk by the ratio of the least integer.
D.21 Two bicycles in a tunnel
The bicycle A went into the tunnel at 4 m/s.
After 24 seconds, the bicycle B went into the tunnel from the opposite side at 6 m/s.
Two bicycles met in the middle of the tunnel.
Find the distance of this tunnel at this time.
After 24 seconds, the bicycle B went into the tunnel from the opposite side at 6 m/s.
Two bicycles met in the middle of the tunnel.
Find the distance of this tunnel at this time.
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