Math problem : CC.18 Management of the party

I became a manager of the party.
I can buy 90 juice exactly with the amount of the budget.
If it is sandwiches, I can buy 36 pieces exactly and if it is cakes, I can buy 40 pieces exactly.
When one juice, one sandwiches, and one cake are made into 1 set for one person, I can buy them for all the members within the budget and 360 yen will remain.
The budget is insufficient if there are more members.

(1) Find the number of participants of the party.

(2) Find the budget.

Math Problem : JJ.51 Triangle and trapezoid

In the figure, triangle ABC is an isosceles triangle and a quadrangle ACDE is a trapezoid.

Find the area of X and Y.

Math Problem : JJ.50 Overlapping of rectangle and circle

Find the area of the shaded portion in the rectangle of the figure.

A and B are the centers of each circle.

Pi is assumed to be 3.14 and the answer should round off the 2nd decimal place.

CC.13 Bagging work by three persons

Three persons, Taro, Jiro, and Hanako carry out bagging work of a certain product.
In order to all products are bagged, it will take 150 minutes by two persons, Taro and Jiro, and it will take 125 minutes by two persons, Taro and Hanako and it will take 600 minutes by Jiro.
Find the time of bagging all products done by Taro.

When Taro and Jiro start bagging first and Hanako will join afterwards, find the minimum time when Hanako must work in order to finish bagging all within 120 minutes.
Answer should be rounded out the decimal point and calculated to the unit of minute.

GG.24 13 persons ordered one confectionery and drink

In a certain store, a cake costs 320 yen, a pudding costs 210 yen, juice costs 70 yen, and tea costs 120 yen.
When 13 persons ordered one confectionery and one cup of drink, respectively, the total amount was 4790 yen.
Find the probable number of persons who ordered the pudding.

EE.2 Water into three tanks

There are three kinds of tanks with equal capacity which are the rectangular prism as shown in the figure.
The side of the tank on which there is the same mark expresses the same length.
The graph expresses a relation with the depth of the water and time when the same amount of water per minute is put in three tanks.
The height of the tank represented by the graph of B is 40 cm.

(1) Find the height of the tank represented by the graph of A.

(2) Find the amount of the water put in per minute.

LL.20 (Deleted) Four different volume of iron balls

Only one heavy ball is included in the balls whose form and size are same.
I think that I will find a heavy ball using an even balance by which heavier ball is found.

For example, when there is only one heavy ball in three balls, it is just once to find certainly a heavy ball by using even balance.

The number of times of using even balance should be lessened as much as possible.
Answer the following questions.
Noted that there is no limit of number of balls to be put on the even balance.

(1) In order to certainly find a heavy ball in 21 balls, find the minimum number of times using the even balance.

(2) Suppose that the even balance can be used only 4 times.
Find the most number of balls in which a heavy ball is certainly found.

LL.18 Tournament of soccer in eight teams

Put in the character or number applicable to following [ ].

8 teams of A~H held the tournament game of soccer in pairing as shown in a figure.

The table shows the sum total of scored points and lost points (opposition’s score) of each team after the end of the tournament.

In the table the portion which we do not know the number anymore is left blank.

In all games victory and defeat was determined with the score difference of one or more points and there was no draw.

(1) At the 1st games, [ ] team won the game of A team vs B team.
[ ] team won the game of C team vs D team.

(2) The sum total of the scored point of E team is [ ] points among blanks in the table and the sum total of the lost points of H team is [ ] points.

(3) [ ] team won [ ] team and won the championship in the final.

Scored points of the team which won the championship in the final are [ ] points and lost points are [ ] points.

K.10 Hexagonal column

The solid of the figure is a hexagonal column whose bottom is a right hexagon.

(1) Find the number of sides parallel to side AB.

(2) Find the number of faces vertical to the face X.

(3) Find the number of faces vertical to the side AG.

DD.36 Library between school and station

Taro and Jiro left the school at the same time and went to the station through the front of library.
Taro ran to the library and walked at 40 m/m from there up to the station.
Jiro walked with the speed of 1/3 of the speed which Taro ran up to the library and arrived at the library 8 minutes later than Taro.
From there, he walked faster by 10 m/m than before.
Then, Taro and Jiro arrived at the station at the same time 20 minutes after leaving the school.
Find the distance from the school to the library, and the distance from the library to the station.

DD.35 Triathlon race

Taro and Jiro participated in the triathlon carrying out 1.5 km of swimming, 40 km of bicycle, and 10 km of running in order.

(1) The time of swimming of Taro was 20 minutes and 50 seconds.
Find the speed per minute of swimming of Taro.

The speed ratio of swimming and pedaling a bicycle of Taro was 3 : 20.
Find the time of the bicycle of Taro.

(2) It was 5 minutes and 20 seconds later than Taro for Jiro to start running.
Since the speed of running of Jiro was quicker than Taro by 32 m/m, Jiro caught up with Taro 34 minutes and 40 seconds after Jiro started running.

Find the ratio of the speed per minute of running of Taro and Jiro.
Find the speed per minute of running of Jiro.
Find the distance from the point where Jiro caught up with the Taro to the goal.

(3) Find the sum total time of three events of Jiro.

JJ.24 Three angles in two figures

Find the degree of angle X, Y, and Z in a figure.

In Fig. 1, quadrangle ABCD is a square and curve is a part of circle with a vertex of the square as a center.

In Fig. 2, triangle ABC is an equilateral triangle and pentagon ADEFG is an equilateral pentagon.