System of equations - 6th grade (11y) - math problems

Number of problems found: 64

Rectangle
The length of one side of the rectangle is three times the length of the second side. What are the dimensions of the rectangle if its circumference 96 cm?
Dividing money
Vilem, Cenek, and Edita divided the money they earned by spreading the leaflet. Vilem got 240 CZK more than Cenek and twice more than Edita. Edita got 400kc less than Vilem.
The fruit basket
The fruit basket is five times heavier than the empty basket. Filled is 20kg heavier than empty. Determine the weight of the fruit in the basket.
Benches
The park has 64 benches. Occupied are by 18 more than empty. How many benches are occupied and empty ?
Guess a fraction
$fractions_1$ Tom was asked to guess a fraction. The sum of 1/2 the numerator and 1/3 of its denominator is 30. If Tom subtracts 36 from its denominator, the fraction becomes 1/3. What is the fraction that Tom was asked to guess? (Leave your answer in simplest form)
The tourist
The tourist came started from the hostel at an average speed of 5km/h. Half an hour later, the bicyclist started along the same route at a speed of 20km/h. How many minutes will a cyclist catch up and how many kilometers will he go?
Pets in ZOO
The zoo have run for pets. They are chickens, pigs and cow. Altogether there has 20 heads and 60 feet. How many chickens and piglets are there?
Wine
A bottle of wine costs 21 euros; and wine is 20 times more expensive than a bottle. How much a bottle cost?
Buns and toasts
Two buns weigh 10 grams more than two toasts. One Bun and two Toast weigh a total of 110 grams. How many grams weigh three toasts? How many grams does a Bun weigh?
Subjects
Student makes a mathematical task for five minutes and the task from biology in twelve minutes. Another day he have homework in math and biology which consists of eleven tasks together. To do the job took hour and a half. How many tasks maked in each subj
Bag
Nelly found interesting point. An empty bag weighs 4 kg less than full. And empty bag is 5 times easier than full. How many kg weigh things in this bag?
Triangle ABC
In a triangle ABC side b measure 10 cm less than the side a and side b is half of the side c. Calculate the length of sides if the circumference of the triangle is 42 cm.
Have solution
The sum of four consecutive even numbers is 96. Determine these numbers.
Can
Watering can full of water weighs 10 kg. Half-full can weighs 5.5 kg. How much weigh can?
Children
Margaret and Zdena weighs the same and Petra 3 kg more. Together weigh 156 kg. How much does they weigh?
Crown coins
Jana saves two-crown and five-crown coins. She has ten coins in the cashier. How many two crowns and how many five crowns shw have if she saved 29 crowns?
Pytagoriade
Two fifth-graders teams competing in math competitions - in Mathematical Olympiad and Pytagoriade. Of the 33 students competed in at least one of the contest 22 students. Students who competed only in Pytagoriade was twice more than those who just compete
Family
Son is 3/5 smaller than the mother. Mother is 99 cm higher than the son. How tall is the mother?
Borrowed book
Jane must as soon as possible return a borrowed book. She figured that when she read 15 pages a day return book in time. Then she read 18 pages a day and then return the book one day before. How many pages should have a book?
Bonbons 2
Kilo sweets will cost 260 CZK. The first type has a price per 320 kg, the second type 240 CZK per kg. How many kilos of both kinds of sweets need to prepare a 100 kg mixture ?