# Equation - examples - page 34

1. Working together
One painter paint the nursery in 10 days, the second in 8 days. How many days will the nursery be painted if they work together?
2. Unknown number 6
Determine the unknown number, which is by 1.5 greater than its fourth.
A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
4. AP 6
Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38
5. Family
Son is 3/5 smaller than the mother. Mother is 99 cm higher than the son. How tall is the mother?
6. Equation
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7. Angles in ratio
The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z.
8. Four friends
Four friends shared the money. Vasek got 1/4 of the total amount. Tonda received 1/3 of the rest of the money, Joe got a half from the second residue and Jirka left 80. How much money get together?
9. Reciprocal equation
Determine the root of the equation: 9/x-7/x=1
10. Linear function
What is the equation of linear function passing through points: a) A (0,3), B (3,0) b) A (-2,-6), B (3,4)
11. Orchard
3/5 of the trees in the orchard are apples, 1/3 are cherries and the remaining five trees are pear. How many trees are in the orchard?
12. Potatoes 6
The farmer brought potatoes to the market. In the first hour he sold two-fifths of the potatoes brought, in the second hour he sold five-sixth of the remaining potatoes, and in the third hour he had sold the last 40kg of potatoes. How many kg of potatoes d
13. Apples 5
In six crates are 45 kg of apples. In five crates were the same amounth and in one crate was 3 kg of apples more. How many kg of apples were in each crate?
14. Equation with abs value
How many solutions has the equation ? in the real numbers?
15. Remuneration
Total remuneration for workers is 47 000 CZK. The second worker received 20% more than the first and third 4000 CZK less than a second employee. How many CZK each received?
16. 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?
17. Sum of three numbers
The sum of three numbers from which second number is 20% smaller than the first number and the third number is 25% smaller than the second number is 96. Determine this numbers.
18. Krkonose CZ
Tourist's rod on the tourist route in the Krkonose was 1/5 of its length into the ground. Snow fell in winter and 1/3 of the length of the rod remained above the snow. Find the height of the snow if the length of the part above the snow is 32 cm greater t
19. Two ages
Gabrielle is 9 years younger than Mikhail. The sum of their ages is 87. What is Mikhail's age?
20. Cat
One-fifth of the monthly pocket money contributes Maros for food for his cat, half of the rest postpone for a new smartphone. The remaining € 8 spend. How much pocket money gets Maros a month?

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