# Algebra - problems - page 100

1. Peter and Paul
Peter and Paul together have 26 years. Four years ago, Paul was twice older than Peter. How much is Paul and how much Peter?
2. Distance problem
A=(x, x) B=(1,4) Distance AB=√5, find x;
3. Banknotes
How many different ways can the cashier payout € 310 if he uses only 50 and 20 euro banknotes? Find all solutions.
4. The pool
The pool contains 220 m3 of water. The pool can be emptied either: a) 10 hours of pipe B and 8 hours of pipe A, or b) 10 hours of pipe A and 7 hours of pipe B. How many cubic meters of water will flow in 1 hour from pipe A and how many from pipe B?
5. Bed time
Tiffany was 5 years old; her week night bedtime grew by ¼ hour each year. If, at age 18, her curfew time is 11pm, what was her bed time when she was 5 years old?
6. Circus
On the circus performance was 150 people. Men were 10 less than women and children 50 more than adults. How many children were in the circus?
7. Inquality
Solve inequality: 3x + 6 > 14
8. Simplify 2
Simplify expression: 5ab-7+3ba-9
9. Parallelogram
Rhomboid (parallelogram) has a longer side of 50 cm long. The size of its one height is four times the size of its second height. Calculate the length of the shorter side of this rhomboid in the centimeters.
10. Banknotes
Eva deposit 7800 USD in 50 banknotes in the bank. They had value 100 USD and 200 USD. How many were they?
11. Reminder and quotient
There are given numbers A = 135, B = 315. Find the smallest natural number R greater than 1 so that the proportions R:A, R:B are with the remainder 1.
12. Balloon and bridge
From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
13. Father and son
Father and son weigh together 108kg. The father weighs 2.6 times more than his son. How much does weight my father and son count?
14. Cows and calves
There are 168 cows and calves in the cowshed. Cows are in nine stalls and calves in four stalls. Same count cows are in every cow stall and three more in each calf stall than in a cow stall. What is the capacity of the stalls for cows and what for calves?
15. Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
16. Curve and line
The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
17. Shopping center
The shopping center buys from the manufacturer bikes at a purchase price of 180 €. It sells them for a sale price of 250 €. However, in the advertising for the sale of these goods, the shopping center spent 20% of the selling price of all bicycles in stock
18. Equations - simple
Solve system of linear equations: x-2y=6 3x+2y=4
19. Train speed
Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of the train (in km/hr), supposing that sound travels at 340 m/s is: