Examples for 9th grade - page 33

Purchase
Mother bought 5 boxes of milk and 7 kg of potatoes and paid a total CZK 147. Aunt bought 7 boxes of milk and 3 kg of potatoes and paid 131 CZK. What is the price of one carton of milk and 1 kg of potatoes? How CZK together would have saved if bought at the
Equations
Solve following system of equations: 6(x+7)+4(y-5)=12 2(x+y)-3(-2x+4y)=-44
Logs
The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it?
A three-digit numbers
Determine the total number of positive three-digit numbers that contain a digit 1.
Unknown number
Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The produ
Mother and daughter 2
The mother is 40 years older than her daughter. How old is the mother if her age is eight thirds age of daughter?
Football league
In the 4th football league plays each of the 16 participants with each opponent twice. For every victory gets 3 points, 1 point for a draw, a defeat none. After the competition was team with 56 points and 8 defeats at 6th place. How many times have won?
Vectors
Vector a has coordinates (7; 16) and vector b has coordinates (15; -7). If the vector c = b - a, what is the magnitude of the vector c?
Cosine
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 19 and 4 and with the hypotenuse 19.416.
Tachometer
Tatra's tachometer shows the initial state 154009 km this morning. Tatra today travel at an average speed of 35 km/h. Determine the function that describes the Tatra's tachometer depending on the time. What is the state of tachometer after 4.8 hours?
Combi-triangle
On each side of the square is marked 2 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square?
Ice cream in cone
In the ice cream cone with a diameter of 3.6 cm is 0.9 dl of ice cream. Calculate the depth of the cone.
Simple interest 4
Find the simple interest if 19590 USD at 4.6% for 242 days. Assume a 360-day year.
Tank
In the middle of a cylindrical tank with a bottom diameter 350 cm is standing rod which is 31 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank?
Freedom
In the city are 2/6 of women married for 4/4 men. What proportion of the townspeople is free (not married)? Express as a decimal number.
Fraction
For what x expression ? equals zero?
Felix
Calculate how much land saw Felix Baumgartner after jump from 22 km above ground. The radius of the Earth is R = 6378 km.
Euler problem
Someone buys a 720 tolars towels. If it was for the same money of 6 more towels, it would be 6 tolars cheaper each. How many were towels?
Trees
Along the road were planted 250 trees of two types. Cherry for 60 CZK apiece and apple 50 CZK apiece. The entire plantation cost 12,800 CZK. How many was cherries and apples?
Coach
Average age of 24 players and a coach of one team is 24 years. The average age of players without a coach is 23 years. How old is the coach?

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