System of equations - practice problems - page 8 of 107
Number of problems found: 2131
- GP - free
For a geometric sequence, an interesting relationship between the first and third terms applies: a1-a3=-1.5 a3-a1=1.5 Calculate the quotient q and the first term a1. - Wands - Wizard
The number promised the wizard Rhododendron that she would teach him a lot about numbers, but he must solve her riddle: My two magic wands measure 63 cm together. One is 7 cm longer. How long are her wands? - Me and my father
My father and I are now 55 years old together. When we are 65 years old together, my father will be four times older than me. How old am I? - Daniel 3
Daniel and Eva earned 180 euros together. Daniel earned 70 euros more than Eva. How much did Daniel earn, and how much did Eva earn? - Three friends 10 Three friends Peter, Tomáš and Jirka earned 4000 CZK working part-time. Peter earned three times more than Tomáš and Jirka earned 500 CZK more than Tomáš. How much did each of them earn?
- Matej 2
Matej, Marko, Milan, and Matúš had a total of 205 football player cards with signatures. Marko has four times more than Matej. Matúš had two times less than Marko. Milan had 20 cards less than Matúš. How many cards did each have? - In the domestic
In the domestic express train, there are 1st and 2nd class carriages. There are 2x more 2nd class carriages than 1st class. There are 10 compartments in each carriage. In 1st class, each compartment has 6 seats, and in 2nd class carriages, there are eight - To the cinema 2
On Tuesday, 20 more visitors came to the cinema than on Monday. On Wednesday, half as many visitors came as on Tuesday. There were a total of 175 visitors to the cinema during these three days. How many were there each day? - Gardener 5
The gardener bought 17 apple trees and 11 pears. He paid a total of €111.65. How many euros did 1 pear cost, if we know that its price was 35 cents higher than the price of 1 apple tree? How much would the gardener pay for 28 apple trees and 15 pears? - Anna had 2
Anna had 2x more than Betka. Cilka had 12 euros more than Anna. Together, they had 92 euros. How much did each have? - Double the number of apples Adam and Bonifác were picking apples. Together they picked 77 kg of apples. How much did each of them collect when Adam collected 5 kg more than twice what Bonifác collected?
- On the board
A problem for dividing two positive numbers was written on the board. David noticed that if he increased the dividend by 2 and the divisor by 7, the quotient would not change. By how much should the divisor be increased so that when the dividend is increa - Three numbers The product of three natural numbers is 600. If we reduced one factor by 10, the product would decrease by 400. If we increased one factor by 5 instead, the product would increase to twice the original value. Which three numbers have this property?
- Preparing the mixture
The seller prepared 25 kg of the mixture for 264 CZK per 1 kg. The first type was 180 CZK per 1 kg and the second was 390 CZK per kg. How much of each did he need? - Received 84200
Jana received a new book. She wants to read it in 8 days. If she read 6 more pages a day, she would read the book two days earlier. How many pages does the book have? - Kilometers 84199
Three friends, Jana, Janett, and Adriana, like to run. On Sunday they all went for a run. Jana ran twice as many kilometers as Žaneta. Adriana ran 3 kilometers more than Žaneta. How many kilometers did Adriana run if the friends ran 11 kilometers together - Parking 84175
There are 96 cars in the parking lot. There are 24 fewer dark cars than light cars. How many light cars are there in the parking lot? - A year ago
A year ago, Jano was twice as old as Lenka. In five years, Jano will be half as old as Lenka. How old is Lenka? - Two workshops Two workshops were supposed to produce 4000 sets of kitchen utensils together. After completing this task, it was found that the first workshop produced 534 sets more than was originally set for it, while the second workshop fulfilled its task by 80%. How
- Four-digit number
Juraj is thinking of a four-digit number that he told us about: (a) Its digit sum is one hundredth of the number that I get by rounding the imaginary number to hundreds. (b) Its last digit is 1 more than the second-to-last. (c) The sum of its last two dig
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