# Examples for 9th grade - page 29

- Siblings

Three siblings had saved up a total of 1,274 CZK. Peter had saved up to 15% more than Jirka and Hanka 10% less than Peter. How much money they saved each one of them? - Concentration

How many grams of 65% and 50% acid is to be mixed to give 240 g acid with a concentration of 60%? - AP 6

Calculate the first five items of an arithmetic sequence if it is given: a_{2}– a_{3}+ a_{5}= 20 a_{1}+ a_{6}= 38 - Glass

Trader ordered from the manufacturer 200 cut glass. The manufacturer confirmed the order that the glass in boxes sent a kit containing either four or six glasses. Total sent 41 boxes. a) How many boxes will contain only 4 glasses? b) How many boxes will co - Numbers at ratio

The two numbers are in a ratio 3:2. If we each increase by 5 would be at a ratio of 4:3. What is the sum of original numbers? - Reducing number

Reducing the an unknown number by 28.5% we get number 243.1. Determine unknown number. - Pedestrian and the cyclist

Pedestrian and cyclist went against each from the two cities that are distant 40 km. Pedestrian started 30 minutes before the cyclist and walk an average speed of 5 km/h. What speed went cyclist when met after 120 minutes from the start of the pedestrian? - Cans

How many cans must be put in the bottom row if we want 182 cans arrange in 13 rows above so that each subsequent row has always been one tin less? How many cans will be in the top row? - Three friends

Peter is eight times older than Rado, Rado is 3 times younger than Joseph. Together they have 120 years. Determine how many are each of them. - Cars motion

From point A car start at the speed of 90 km/h. Against it departs from the point B at the same time another car at 60 km/h. For how long and where they met if the distance between A and B is 180 km? - Family parcels

In father will he divided the land so that the older son had three bigger part than younger son. Later elder son gave 2.5 ha field to younger and they had both the same. Determine the area of family parcel. - Dining room

The dining room has 11 tables (six and eight seats). In total there are 78 seats in the dining room. How many are six-and eight-seat tables? - Summerjob

Albert, Beny, Cyril and Dan worked on summerjob. From the total revenue Albert received 2/5, Beny 1/6 , 3/10 Cyril and Dan the rest which is 324 euros. How many euros earned every one of them? - Equations

Solve following system of equations: 6(x+7)+4(y-5)=12 2(x+y)-3(-2x+4y)=-44 - Freight train

The train carries 525 tons of limestone in 29 wagons. Wagons are 15 tonne and 20 tons. How many is 15 ton and how many is 20 ton wagons? - A three-digit numbers

Determine the total number of positive three-digit numbers that contain a digit 1. - Triangular prism

The base perpendicular triangular prism is a right triangle whose hypotenuse measures 13 cm and one cathetus 2 cm. Height of the prism is equal to 10/7 of the perimeter of the base. Calculate the surface area of prism. - Unknown number

Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The produ - Football league

In the 4th football league plays each of the 16 participants with each opponent twice. For every victory gets 3 points, 1 point for a draw, a defeat none. After the competition was team with 56 points and 8 defeats at 6th place. How many times have won? - Cosine

Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 19 and 4 and with the hypotenuse 19.416.

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