# Examples for secondary school students - page 58

1. Vegan shop
To the shops brought together 23.2 kg of goods, fruits, vegetables and nuts. fruit was 4.7 kg more than vegetables, nuts was 1.5 kg less than the fruit. Determine the amount of fruits, vegetables and nuts.
2. Determine AP
Determine the difference of the arithmetic progression if a3 = 7, and a4 + a5 = 71
3. Elimination method
Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
4. Geometric seq
Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient.
5. Potatoes bags
I have three bags with 21 kg potatoes. The first bag is 5.5 kg more than in the second bag and the third is 0.5 kg more than in the second bag. Determine how many kgs of potatoes is in each bag.
6. 925 USD
Four classmates saved an annual total 925 USD. The second save twice as the first, third 35 USD more than the second and fourth 10 USD less than the first. How USD save each of them?
7. Dividing money
Imrich, Daniel and Dezider shared an unknown amount in the ratio 1:2:4, where Dezider received 750 euros more than Imrich and Daniel got half as much as Dezider. Determine an unknown amount of money and determine the amounth that got Imrich, Daniel and De
8. 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%?
9. Scalene triangle
Solve the triangle: A = 50°, b = 13, c = 6
10. Quotient
Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4.
11. Find the area
Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft
12. Three friends
Danica, Lenka and Dalibor have altogether 96 kg. Lenka weighs 75% more than Dalibor and Danica weighs 6 kg more than Dalibor. Determine the weight of Danice, Lenka and Dalibor.
13. Conical area
A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.
14. Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle conta
15. Resultant force
Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
16. Unknown number
I think number. If subtract from the twelfth square the ninth square I get a number 27 times greater than the intended number. What is this unknown number?
17. Two lands
The common area of the two neighboring lands is 964 m2. The second land is 77 m2 smaller than twice the size of the first land. Find the areas of each land.
18. Competition
15 boys and 10 girls are in the class. On school competition of them is selected 6-member team composed of 4 boys and 2 girls. How many ways can we select students?
19. The gardener
The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy?
20. Q of GP
Calculate quotient of geometric progression if a1=5 a a1+a2=12.

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.