System of equations - high school - practice problems - page 15 of 44
Number of problems found: 878
- wheat 20833
Mr. Vávra sows wheat and rye for a total of 28 ha. Rye sows two and a half times the area of wheat. How many ha sow wheat and how much rye? - Individual 20463
There are 59 pupils in the 9th grade. In 9A, there are 15% more pupils than in 9B. In 9C, there are 20% fewer than in 9B. How many pupils are in individual classes? - Contestants
The three best contestants are to divide the total prize of CZK 4,200. The second gets 20% more than the third. And the first one gets 200 CZK less than the second and the third together. How much will everyone get? - Together 20433
Pavel received half as much money from his parents as Petr and Milan and half as much as Pavel. How much did all the boys get together? The parents gave Milan CZK 1,350. - Circumference 20323
A triangle with sides a, b, and c whose circumference is 26 cm is true: ratio a:b is 4:3, and ratio b:c is 1:2. Find the lengths of the sides of this triangle. - Bent scale
Monica weighed 52 kg. Sara 54 kg. Together they weighed 111 kg. They noticed that the needle on the scale was bent. How much did they really weigh? - Cooperative 19973
The cooperative farmers harvested 300 tons of grain. Wheat was 25% more than oats, and rye was 96 tons less than wheat and oats combined. How many tons of wheat, rye, and oats did the cooperative harvest? - Cherries 19903
There are pears, apples, and cherries in the alley. There are a total of 1,075 trees. Pear is twice as much as apple, and cherry is 30% more than apple. How many trees are there? - Substitution 19793
Calculate in arithmetic sequence a1, d, s7, if: a1 + a4 + a6 = 71 a5 - a3 - a2 = 2 Hint: Use the substitution method when solving the system. Pay due attention to the "minus" signs in the second equation of the system. - Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, and √13cm. Calculate the surface and volume of the block. - Vector perpendicular
Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1) - Trapezoid: 18703
In the ABCD trapezoid: | AD | = | CD | = | BC | a | AB | = | AC |. Determine the size of the delta angle. - Speedometer 18693
The Macháček family went on a 3-day trip to Třeboň. They didn't want to get too tired but wanted to see a lot. Therefore, they drove at a walking pace, and at the end of the 3rd day, they measured 90 km on the speedometer. On the second day, they traveled - Successively 18673
Vašek likes to go to the forest to pick mushrooms. He collected them successively for 3 days. Day 1 found seven less than Day 3. On the second day, he collected eight more than on the third day. He collected a total of 79 mushrooms. How much did he collec - The tourist
The tourist wanted to walk the route 16 km at a specific time. He, therefore, came out at the necessary constant speed. However, after a 4 km walk, he fell unplanned into the lake, where he almost drowned. It took him 20 minutes to get to the shore and re - Vector equation
Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent - Porcelain 18063
Four cups and one porcelain saucer cost € 140. Two cups and five saucers cost € 160. How much is a cup? - Equations 18023
Solve a system of equations with four unknowns: 2a + 2b-c + d = 4 4a + 3b-c + 2d = 6 8a + 5b-3c + 4d = 12 3a + 3b-2c + 2d = 6 - Fourth-week 17783
They earned CZK 113,400 in the shop in four weeks. The first and fourth-week sales were the same, the second week 10% higher than the first week and the third week 5% lower than the first week. How much did they earn each week? - One-fifth 17753
The store stacked two hundred boxes of washing powder in three piles. There were 13 more boxes in the first pile than in the second pile, one-fifth more in the second pile than in the third pile. How many boxes were in which pile?
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