9th grade (14y) + system of equations - examples
- Three shapes
1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
The grandfather is three years older than an grandmother. The average age of the grandmother, the grandfather and their seven grandchildren is 28 years. The grandchildren have a total of 105 years. Calculate how old is grandfather.
- Two workers
Two workers make 138 parts/items. The first one produces 30% more than the second. How many items will each produce?
The length of the rectangle is 8 smaller than three times the width. If we increase the width by 5% of the length and the length is reduced by 14% of the width, the circumference of rectangle will be increased by 30 m. What are the dimensions of the rectan
- Mr and Mrs
Mr. Calda and Mrs. Cald have a total of 139 years. How many years have when we know that Mr. Calda is 9 years older than Mrs. Cald
- Dividing money
Thomas, Honza and Vasek are to divide 1220kč. Honza got 25% more than Thomas. Vasek 20% less than Thomas. How CZK each got?
How long are the trapezoid bases with area 24 cm2 and height 3 cm. One base is 3 times longer than the shorter.
- Lord Ram
When lord Ram founded the breed white sheep was 8 more than black. Currently white sheep are four times higher than at the beginning and black three times more than at the beginning. White sheep is now 42 more than the black. How many white and black sh
The football team has 11 players. Their average age is 21 years. During the match due to injury, one player withdraws and the average age of the team is 20. How old was injured player?
- Exam average
Average of marks that have on the certificates students of 8.A class in mathematics is exactly 2.45. If we did not add 1 and 3 of sutdents Michael and Alena, who arrived a month ago, it would average exactly 2.5. Determine how many students have class 8.
Three siblings Helena, Oliver and George split the bag with candies on merit in the ratio 1:6:3. How many candies should each get if in bag were 210?
- Barrel of oil
Barrel of oil weighs 282 kg. When it mold 56% oil, weighed 138 kg. What is the mass of the empty barrel?
One meter of the textile were discounted by 2.4 USD. Now 6 m of textile cost as before 3 m. Calculate the old and new price of 1 m of the textile.
Clerk got to pay 1200 Euros in banknotes of 50 and 200 Eur. Total got 9 banknotes. How many was which?
- Three friends
Three friends squirrels together went to collect hazelnuts. Zrzecka he found more than twice Pizizubka and Ouska even three times more than Pizizubka. On the way home they talked while eating and was cracking her nuts. Pizizubka eaten half of all nuts whi
There is 28 students in a class. From mathematics was'nt worse mark than 2. Average mark in mathematics was 1.4643. How many students have mark 1 and how many mark 2?
How much 60% solution and how much 35% solution is needed to create 100 l of 40% solution?
Family has 4 children. Ondra is 3 years older than Matthew and Karlos 5 years older than the youngest Jane. We know that they are together 30 years and 3 years ago they were together 19 years. Determine how old the children are.
- BW-BS balls
Adam has a full box of balls that are large or small, black or white. Ratio of large and small balls is 5:3. Within the large balls the ratio of the black to white is 1:2 and between small balls the ratio of the black to white is 1:8 What is the ratio of.
- Waiting room
In the waiting room are people and flies. Together they have 15 heads and 50 legs (fly has 6 legs). How many people and flies are in the waiting room?