System of equations - high school - practice problems - page 13 of 45
Number of problems found: 882
- Triple and quadruple rooms
Up to 48 rooms, some of which are triple and some quadruple, accommodated 173 people so that all beds are occupied. How many triple and how many quadruple rooms were there? - Individual 28401
In the first and second years, there are 58 pupils in a pile. In the first and third years, there are 57 pupils. In the second and third years, there are 59 pupils. How many students are there: a) In all of them, to the dromedary, b) In individual classes - Vector v4
Find the vector v4 perpendicular to the vectors v1 = (1, 1, 1, -1), v2 = (1, 1, -1, 1) and v3 = (0, 0, 1, 1) - Quarantine cupcakes
Mr. Honse was baking quarantine cupcakes. Mrs. Carr made twice as many as Mr. Honse. Ms. Sanchez made 12 cupcakes, more than Mr. Honse. If they put all their cupcakes together (which they can't because. of quarantine!), they would have 108 cupcakes. How m
- 2 cyclists and car
One cyclist rides at a constant speed over a bridge. It is 100 meters long. When he is 40 meters behind, he meets an oncoming cyclist riding at the same speed. The car travels along the bridge in the same direction as the first cyclist at a speed of 70 km - Lottery - eurocents
Tereza bets in the lottery and finally wins. She went to the booth to have the prize paid out. An elderly gentleman beside him wants to buy a newspaper but is missing five cents. Tereza is in a generous mood after the win, so she gives the man five cents - Traveling 27833
The truck drove at an average speed of 20 km/h and left Prague toward Liberec. At the same time, a bus left with him, traveling at an average speed of 30 km/h, and it arrived in Liberec 2 hours earlier than the truck. What is the distance between Prague a - Candles
Before Christmas, Eva bought two cylindrical candles - red and green. Red was 1 cm longer than green. She lit a red candle on Christmas Day at 5:30 PM, lit a green candle at 7:00 PM, and left them on fire until it burned. At 9:30 PM, both candles were the - Intersections 3
Find the intersections of the circles x² + y² + 6 x - 10 y + 9 = 0 and x² + y² + 18 x + 4 y + 21 = 0
- Thirty-five 27011
Thirty-five applicants applied for the company's audition. In the first round, they were divided into 3 groups. In the first group, there are 3 people fewer than in the second. In the third, there are 2 more people than in the second. How many candidates - Lookout tower
How high is the lookout tower? If each step was 3 cm lower, 60 more were on the lookout tower. If it were 3 cm higher again, it would be 40 less than it is now. - Coordinates
Determine the coordinates of the vertices and the area of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0 - The tower
The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands? - Three-quarters 25931
Jarek went strawberry picking for a day. In the morning, he collected two-fifths of the required amount; in the afternoon, he collected 5 kg less than in the morning. In total, he collected three-quarters of the required amount. How many kilograms of stra
- Summands
We want to split the number 110 into three summands so that the first and the second summand are in ratio 4:5, and the third with the first are in ratio 7:3. Calculate the smallest summands. - Accommodated 25881
Fifty-one students are accommodated in the tourist hostel in 15 four-bed and three-bedrooms. How many rooms are there if there are 2 spaces left after housing? a) There are four-bed rooms. b) There are three-bed rooms. - Cyclist 25591
The cyclist rode 44 km and 400 m in three days. In the first hour, he covered the course 5% longer than in the second hour, and in the third hour, he covered 1 km more than in the first hour. How many km did he travel in the third hour? - Water mixing
We have 520 ml of hot water and 640 ml of water at 48°C. What is the temperature of approximately hot water when the resulting mixture has a temperature of 65°C? - Columns of two and three
When students in one class stand in columns of two, there is none left. When he stands in columns of three, there is one student left. There are five more double columns than three columns. How many students are in the class?
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