# Examples for 9th grade - page 82

- Elimination method

Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15 - ATC camp

The owner of the campsite offers 79 places in 22 cabins. How many of them are triple and quadruple? - Potatoes bags

I have three bags with 21 kg potatoes. The first bag is 5.5 kg more than in the second bag and the third is 0.5 kg more than in the second bag. Determine how many kgs of potatoes is in each bag. - 925 USD

Four classmates saved an annual total 925 USD. The second save twice as the first, third 35 USD more than the second and fourth 10 USD less than the first. How USD save each of them? - Three cubes

The body was created by gluing three identical cubes. Its volume is 192 cm^{3}. What is its surface in dm^{2}? - Diagonals

Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus. - Summerjob

Three students participated in the summerjob. Altogether they earn 1780, -. Peter got a third less than John and Paul got 100,- more than Peter. How much got every one of them? - Tour

35 people went on a tour and paid 8530, -. Employees pay 165, and family members 310. How many employees and how many family members went to the tour? - Collecting day

At collecting day at school pupils of three classes took total of 1063 kg of paper. Class B collected half more than A Class and class C 55 kg more than B. How many kg of paper collected each class? - Red balls

In the bag there are 3 red, 12 blue and 8 green balls. How many red balls we must be attached to the bag if we want the probability of pulling out the red balls was 20%? - Trees

Along the road were planted 250 trees of two types. Cherry for 60 CZK apiece and apple 50 CZK apiece. The entire plantation cost 12,800 CZK. How many was cherries and apples? - Quotient

Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4. - Family party

Anna has 5 €, Anezka has 4,60 € and for all the money they want to buy desserts for a family party. They decide between cakes and pinwheel: The pinwheel is € 0.40 more expensive than the cake, and the cakes can be bought for all the money by a third more t - Equilateral triangle ABC

In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle conta - Coach

Average age of 24 players and a coach of one team is 24 years. The average age of players without a coach is 23 years. How old is the coach? - Three friends

Danica, Lenka and Dalibor have altogether 96 kg. Lenka weighs 75% more than Dalibor and Danica weighs 6 kg more than Dalibor. Determine the weight of Danice, Lenka and Dalibor. - Conical area

A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation. - Drying apples

By drying, apples lose 85% of their weight. How many kgs of dried apples do we get from 820 kilograms of fresh? - Two lands

The common area of the two neighboring lands is 964 m^{2}. The second land is 77 m^{2}smaller than twice the size of the first land. Find the areas of each land. - Three granaries

Three granaries hold 7,800 metric cent (q) of grain. In the first, 70 tonnes of grain was more than the second and in the third it was 120 tonnes less than in the second. How many grain were in each granary?

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