# System of equations - 7th grade (12y) - math problems

#### Number of problems found: 177

- Angles of a triangle

In the triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle. - Rectangles - sides

One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm^{2}. What are the dimensions of the original rectangle? - Coffee

In-stock are three kinds of branded coffee prices: I. Kind. .. .. .205 Kc/kg II. Kind. .. .. .274 Kc/kg III. Kind. .. .. 168 Kc/kg Mixing these three species in the ratio 8:5:6 create a mixture. What will be the price of 100 grams of this mixture? - Watching TV

One evening 2/3 students watch TV. Of those students, 3/8 watched a reality show. Of the students that watched the show, 1/4 of them recorded it. What fraction of the students watched and recorded reality tv. - Brunette

Of the girls who attend primary school are 30% blondes and 70% brunette. 81% blondes and 19% brunette has blue eyes. How many girls attending school altogether if 470 girls has blue eyes? - Bonbons 2

Kilo sweets will cost 260 CZK. The first type has a price per 320 kg, the second type 240 CZK per kg. How many kilos of both kinds of sweets need to prepare a 35 kg mixture ? - Vacation

Parents piggybacking children on vacation to its grandmother and grandfather at a city distant 150 kilometers. They agreed to meet halfway. Parents will be travel at 90 km/h, grandmother and grandfather at 60 km/h. Parents depart at 12:00 hours. When gran - Pytagoriade

Two fifth-graders teams competing in math competitions - in Mathematical Olympiad and Pytagoriade. Of the 33 students competed in at least one of the contest 22 students. Students who competed only in Pytagoriade was twice more than those who just compete - Sales of products

For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold? - Shoes

Peter decided to measure shoes size of his three friends. Measured accurately and wrote as follows: Venda and Jenda together 52 cm Jenda and Zdenda together 58 cm Zdenda and Venda together 54 cm a) How long measures Vendy, Jenda and Zdenda shoes together? - Forestry workers

In the forest is employed 56 laborers planting trees in nurseries. For 8 hour work day would end job in 37 days. After 16 days, 9 laborers go forth? How many days are needed to complete planting trees in nurseries by others if they work 10 hours a day? - Rings groups

27 pupils attend some group; dance group attends 14 pupils, 21 pupils sporty group and dramatic group 16 pupils. Dance and sporting attend 9 pupils, dance and drama 6 pupil, sporty and dramatic 11 pupils. How many pupils attend all three groups? - The farmer

The farmer brought potatoes to the market. In the first hour he sold two-fifths of the potatoes brought in, in the second hour he sold five-sixths of the remaining potatoes, and in the third hour, he sold the last 40 kg of potatoes. 1. Express a fraction - Lentilka

Lentilka made 31 pancakes. 8 don't fill with anything, 14 pancakes filled with strawberry jam, 16 filled with cream cheese. a) How many Lentilka did strawberry-cream cheese pancakes? Maksik ate 4 of strawberry-cream cheese and all pure strawberry pancakes - Rectangle - sides 3

If in the rectangle ABCD we enlarge the side a by 5 cm and decrease the side b by 2 cm, the rectangle area will be reduced by 5 cm². When we decrease the length of the side a by 4 cm and and at the same time we increase the length of side b by 3 cm we inc - Solution

In 469 dl red solution is 84 dl red color and in 102 dl blue solution is 52 dl blue color. How many dl of red and blue dl color solution must be mixed to get a mixture of 247 dl contain 116 dl of color? - Car rent

Rental cars are paid a fixed daily fee plus 16 cents for each kilometer traveled. Samuel want to rent a car for a day and worked out that will pay 175 euros. When paying he got a 20% discount on the daily fee, the cost per kilometer is unchanged. Samuel t

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