System of equations - 7th grade (12y) - math problems

Number of problems found: 176

Christmas or Easter
Please calculate this example by the Venn equation. They asked 73 students whether they like Christmas or Easter. 34 of them like one of the holidays. 39 loves Easter. There are twice as many students who wish both holidays than those who only love Easter
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.
Age question
Jano is three times older than Zdeno. Zdeno is 12 years younger than Janko. How old is Jano and how old is Zdeno?
Flowerbed
Ondra digs the bed in 20 minutes. Cuba in 30 minutes. For how long do they dig together?
Isosceles triangle
In an isosceles triangle, the length of the arm and the length of the base are in ration 3 to 5. What is the length of the arm?
Supplementary angles
One of the supplementary angles is larger by 33° than the second one. Calculate the angles size.
Gasoline tank 2
A gasoline tank is 1/6 full. When 25 liters of gasoline were added, it became 3/4 full. How many liters more is needed to fill it? Show your solution.
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?
Grandfather and grandmother
The old mother is 5 years younger than the old father. Together they are 153 years old. How many years has each of them?
Two trains
There were 159 freight wagons on the railway station creating 2 trains. One had 15 more wagons than the other. How many wagons did each train have?
Unknown numbers
The sum of two consecutive natural numbers and their triple is 92. Find these numbers.
Simple equations
Solve system of equations: 5x+3y=5 5x+7y=25
Boys and girls
There are 48 children in the sports club, boys are 10 more than girls. How many girls go to the club?
Odd numbers
The sum of four consecutive odd numbers is 1048. Find those numbers ...
Testing
Students of high school have 10 points for each good solved task. The wrong answer is deducted by 5 points. After solving 20 tasks, student Michael had 80 points. How many tasks did he solve correctly and how many wrong?
Boys and girls 2
The ratio of boys to girls in math club is 4:3 . After 8 more girls joined the Club, the ratio become 1:1. How many members are there in the club now?
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)
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?
Every day 7 pages
Adelka reads the book every day 7 pages. When she reads one more page a day she will read it three days earlier. How long will Adelka read a book? How much does a book of pages have?
Sales of products
For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold?