# System of equations - high school - math problems

1. Divide 8 Divide 6840 by x y and z, in such a way that x has twice as much as y, who has half as much as z
2. An animal shelter An animal shelter spends \$5.50 per day to care for each bird and \$8.50 per day to care for each cat. Nicole noticed that the shelter spent \$283.00 caring for birds and cats on Wednesday. Nicole found a record showing that there were a total of 40 birds and
3. Touch x-axis Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
4. Triangle 42 Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is measure of triangle BCA=?
5. Sides of right angled triangle One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
6. Nine books Nine books are to be bought by a student. Art books cost \$6.00 each and biology books cost \$6.50 each . If the total amount spent was \$56.00, how many of each book was bought?
7. The farm The farm harvested 390 tons of grain. Wheat was 15% more than barley, and rye was 126 tons less than wheat and barley combined. How many tons of wheat, how many tons of barley, and how much rye did the team get?
8. Three-day trip The cyclist on three-day trip travel 30% of the total route on the first day, 3/5 of the rest on the second day and 35 km on the third day. How many kilometers did travel cyclists each day and how many?
9. Gasoline-oil ratio The manufacturer of a scooter engine recommends a gasoline-oil fuel mixture ratio of 15 to 1. In a particular garage, we can buy pure gasoline and a gasoline-oil mixture, which is 75% gasoline. How much gasoline and how much of the gasoline-oil mix do we
10. Potatoes For three days the store sold 1400 kg of potatoes. The first day they sold 100 kilograms of potatoes less than the second day, the third-day three-fifths of what they sold the first day. How many kgs of potatoes sold every day?
11. Two math problems 1) The sum of twice a number and -6 is nine more than the opposite of that number. Find the number. 2) A collection of 27 coins, all nickels, and dimes, is worth \$2.10. How many of each coin are there? The dime, in United States usage, is a ten-cent coin
12. A man 2 A man divides \$10,000 into two investments, one at 10% and the other at 30%. Find how much is invested at each rate so that the two investments produce the same income annually.
13. GP - three members The second and third of a geometric progression are 24 and 12(c+1) respectively, given that the sum of the first three terms of progression is 76 determine value of c
14. Mixing water The 30-liter container should we fill with water at 60 degrees Celsius. How many liters of water 80 degrees C hot and how many liters of water 20 degrees Celsius warm we have to mix?
15. Legs Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
16. 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?
17. Together m+w Women 30%. Men are 360 more. How many are together?
18. Rectangular triangle The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
19. Sheep and cows There are only sheep and cows on the farm. Sheep is eight more than cows. The number of cows is half the number of sheep. How many animals live on the farm?
20. Two cubes The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes.

Do you have an interesting mathematical word problem 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 the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...

Do you have a system of equations and looking for calculator system of linear equations?