Algebra - math word problems - page 287 of 305
Number of problems found: 6095
- Number divisor proof
The natural number n has at least 73 two-digit divisors. Prove that one of them is the number 60. Also, give an example of the number n, which has exactly 73 double-digit divisors, including a proper justification. - MO C–I–1 2018
An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones. - Tree planting
Štěpán is planting trees. If he had planted 12 trees every hour instead of 9 trees, he would have finished 1 hour earlier. How many stems should he plant? - Average points
Fifty students took a math test. The average number of points was 68. The top 10 students scored 100 points. What is the average number of points for the remaining 40 students? - Tractor 19
A tractor plows a field in 48 hours using a plow with 5 blades. How long will it take it to plow the same field with a plow with 6 blades of the same width, while maintaining the same tractor speed? - Two alloys
Two alloys, Y and Z, are each made up of zinc, tin, and copper. In alloy Y, the ratio of zinc to tin is 2:5, and the ratio of copper to tin is 4:3. Find the ratio of copper:zinc:tin in alloy Y. - Alcohol solutions
We have to produce 2 liters of 60% alcohol from 55% and 80%. How many of these will we use in the solution? - Worker production
Eight workers produce 2048 products per shift. In how many hours would ten workers produce the same amount of products? (shift is 8 hours) - A 36
A 36 g sample of the substance contains 91% water. After drying, the weight of the sample was reduced to 18 g. What percentage of water is now in the sample? - Coins
The money - -coins are minted from the hardest bronze, which contains copper and tin in a ratio of 41:9. How much copper and tin are in 2kg of bronze money? - Working together
Two people will do the work in 12 days. They worked together for eight days. Then only one worked for ten days. How many days would each of them do the work if he worked alone? - Hectares of forest
Twelve workers plant 24 ha of forest in 6 days. How many days will 15 people and 12 people plant in the same area? - Pouring alcohol
100 liters of alcohol has 70% How many liters of water must be added to have 60% alcohol? - The hiker
The hiker will travel 40% of the route on the first day and 1/3 of the rest on the second day. Last day 30 km. What was the length of the 3-day trip? How many kilometers did he walk each day? - Four workers
Four workers lay on the gym floor for six hours. After an hour of working together, one of the workers went to the doctor. How long will it take for the remaining three workers to complete their work? - Clogging
How much distilled water must the pharmacist add to 30g of a 30% hydrogen peroxide solution to obtain a 3% solution for clogging? - Alcohol
How many cubic centimeters of 96% alcohol is needed to obtain 0.75 liters of 40% alcohol? - Dice unit probability
We roll two dice. One is 6-walled, and the other is 8-walled. What is the probability that at least one unit will fall? - Combinations - elements
If we increase the number of elements by 1, the number of combinations of the third class without repetitions increases by 10. How many elements do we have? - Five number code
I forgot a five-digit code on the bag. I remember that it was a symmetric number, and the sum of its digits was 22. Write down all the numbers that can be coded.
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