# Equation - examples - page 34

1. Geometric sequence 5
About members of geometric sequence we know: ? ? Calculate a1 (first member) and q (common ratio or q-coefficient)
2. Cost reduction
Two MP3 players whose price was equal to originally have been discounted the first by 20%, the second by 35%. After the price reduction was the difference in their prices 750, - CZK. What was the original price of each of the two players?
3. How old
The student who asked how many years he answered: "After 10 years I will be twice as old than as I was four years ago. How old is student?
4. Two numbers
The sum of the two numbers is 1. Find both numbers if you know that half of the first is equal to one seventh of the second number.
5. Rabbits 3
Viju has 40 chickens and rabbits. If in all there are 90 legs. How many rabbits are there with Viju?
5 of the same bread has the same weight as three bread and 4 kg of fruit. What weight has one bread?
7. Ruler
How far from Peter stands 2m hight John? Petr is looking to John over ruler that keeps at arm's distant 60 cm from the eye and on the ruler John measured the height of 15 mm.
8. Unknown number 5
Daniel think an integer. When he change this number at a ratio of 2:5 he got number 2.8. Determine what number think Daniel.
9. Glass
Trader ordered from the manufacturer 200 cut glass. The manufacturer confirmed the order that the glass in boxes sent a kit containing either four or six glasses. Total sent 41 boxes. a) How many boxes will contain only 4 glasses? b) How many boxes will co
10. Tickets
On the football tournament ticket cost 45 Kc for standing and 120kč for sitting. Sitting spectators was 1/3 more than standing. The organizers collected a total 12 300 Kc. How many seated and standing seats (spectators)?
11. VCP equation
Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
12. Infirmary
Two thirds of children from the infirmary went on a trip seventh went to bathe and 40 children remained in the gym. How many children were treated in the infirmary?
13. Primes 2
For what primes p,q,r is true: p2-(q+r)2=647
14. Bags
The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights.
15. Novak
Novak needed to dig up three of the same pit in the garden. The first pit dug father alone for 15 hours. His second dig son helped him and it did that in six hours. The third pit dug son himself. How long it took him?
16. 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?
17. Family
Son is 3/5 smaller than the mother. Mother is 99 cm higher than the son. How tall is the mother?
18. AP 6
Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38