Algebra - problems
- Equation 15
Solve equation with variables on both sides:
- Brick weight
Half the weight of a brick plus 20 pounds is equal to 1/3 the weight of the brick plus 30 pounds. How much does the brick weigh?
- Quadrangular pyramid
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
- 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?
Susan's age will be after 12 years four times as much as twelve years ago. How old is Susan now?
- Number unknown
Adela thought the two-digit number, she added it to its ten times and got 407. What number does she think?
- Unknown numbers
The sum of two consecutive natural numbers and their triple is 92. Find these numbers.
solve equations by substitution: x+y= 11 y=5x-25
- Tangent 3
In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm.
- Simple equations
Solve system of equations: 5x+3y=5 5x+7y=25
- Red balls
In the bag there are 3 red, 12 blue and 8 green balls. How many red balls we must be attached to the bag if we want the probability of pulling out the red balls was 20%?
- Wagons and cranes
Several of the same cranes unloaded 96 wagons. If there were 2 more cranes there would be less 8 wagons for each crane. How many cranes were here?
In the first round of slalom fell 15% of all competitors and in the second round another 10 racers. Together, 40% of all competitors fell. What was the total number of competitors?
- Free fall
How long does the stone fall freely into a depth of 80m? What speed will it hit the bottom of the abyss?
- Mother and daughter
The mother is four times older than her daughter. Five years ago, her daughter was seven times younger than her mother. How many years do they have now?
- Family 8
Father is 38 years old, daughter 12, son 14. How many years will father have as many years as his children together?
- Z9–I–4 MO 2017
Numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage and the largest of each of the three was equal to the sum of the remaining two. The conducto
- Big number
hat is the remainder when dividing number 10 to 47 - 111 by number 9?
A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ?
- Inscribed circle
The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.