System of equations - examples - page 26
- Car driver
The car driver is in town A and is scheduled to be in town B at a specified hour. If it travels at an average speed of 50km/h, it will arrive in city B 30 minutes later. But if he travels at an average speed of 70km/h, he would arrive half an hour earlier
- The train
The train passed the observer in the 20s and passed through a 1500m tunnel in 2 minutes. Calculate the speed (km/h) and train length.
- Three points 2
The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
- Utopia Island
A probability of disease A on the island of Utopia is 40%. A probability of occurrence among the men of this island, which make up 60% of all the population (the rest are women), is 50%. What is the probability of occurrence of A disease among women on Uto
- Two diggers
Two diggers should dig a ditch. If each of them worked just one-third of the time that the other digger needs, they'd dig up a 13/18 ditch together. Find the ratio of the performance of this two diggers.
- Four numbers
The first number is 50% second, the second number is 40% third, the third number is 20% of the fourth. The sum is 396. What are the numbers?
Mother bought 21 desserts on the occasion of Mirka's birthday one tips was 9 CZK and the kremlin cost 12 CZK. For all desserts, she paid 213 CZK. How many kremlins and how many tips mums did buy?
Three years ago, the triplets Pavel, Petr, and Luke and their five-year-old sister Jane had together 25 years. How old is Jane today?
- Highway tunnel
The highway tunnel was built from two ends in the north-south direction. The average daily performance of the "northern party" rasters was higher than the average daily power of the "southern party" of the rasters. After 55 business days, both parties met.
- AP RT triangle
The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
- Six-sided polygon
In a six-sided polygon. The first two angles are equal, the third angle is twice (the equal angles), two other angles are trice the equal angle, while the last angle is a right angle. Find the value of each angle.
- Father 7
Father is 6 times older than his son. After 4 years, the father will only be 4 times older. What are their present ages?
- Two resistors
Two resistors when they give 25 ohms in series and 4 ohms in parallel what the values of
- The sides
The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it.
- Boys to girls
The ratio of boys to girls in a party is 3:5 . If 6 more boys arrived and 4 girls left the party, the ratio of boys to girls would be 5:6 . How many are in the party originally?
- Flowers 2
Cha cruz has a garden. The ratio roses to tulips is 2 : 5, the ratio of roses to orchids is 7 : 6. Cha cruz wonders what the ratio of tulips to orchids is. If Cha cruz has 183 plants, how many of each kind are there?
- New ratio
The ratio of ducks and chicken in our yard is 2 : 3. The total number of ducks and chickens together is 30. Mother gave 3 of the chickens to our neighbor. What is the new ratio now?
- Square into three rectangles
Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.
At the summer camp, there are 41 chalets. Some rooms are 3-beds, some 4-beds. How many campers from 140 are living in 3-bed?
- Barrel with water
The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel.
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