# System of equations - math word problems

1. Algebrogram
Solve algebrogram: mama+anna=vari How many solutions are?
2. Angle
Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence.
3. Angle in RT
Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions.
4. Three friends
Three friends divided the profit 104,650 CZK, so that for every 4 CZK, which got the first friend equals 5 crowns for second and for every 9 CZK, which got the second equals 16 CZK for third. Question: Who got the most and how much.
5. Money duo
Julius and Mark have together 45 euros. Mark has 50% more money than Julius. Determine the amount of money that have Mark and Julius.
6. Rectangle
Perimeter of rectangle is 48 cm. Calculate its dimensions if they are in the ratio 5:3 (width:height)
7. Linear system
Solve this linear system (two linear equations with two unknowns): x+y =36 19x+22y=720
8. Price saleoff
Shoes standing y euros. At first they were discounted by 12% and then 50% of the new amount. After this double cheapening the cost was exactly 22 euros. Determine the original price of shoes.
9. Difference of two number
The difference of two numbers is 20. They are positive integers greater than zero. The first number raised to one-half equals the second number. Determine the two numbers.
10. 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.
11. Lighthouse
The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow shorter by 3 meters. How tall is the lighth
12. Money
Peter has 2x more money than Michael. But if Peter gave Michael € 16 Michael would have 3.5 times more money than Peter. Determine how much money was originally Peter and how much Michael.
13. The rectangle
Determine the area of the rectangle where the length and width are in the ratio 5:2 and its length is 7.5 cm longer than its width. Determine also its length and its width.
14. Unknown amount of money
Damian and Denis split an unknown amount in the ratio of 5:4 . Damian got six euros more than Denis. Calculate an unknown amount. Determine how much money got Damian and how Denis.
15. Table
The circumference of the rectangle table is 420 cm. Length to width ratio is 5:2 . Calculate table dimensions and dimensions reduced in the ratio 3:5
16. 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.
17. Belgium vs Italy
Belgium played a match with Italy and Belgium win by 2 goals. The match fell a total 6 goals. Determine the number of goals scored by Belgium and by Italy.
18. 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
19. Threesome
Dana, Dalibor and Michael have a combined 57 years. Dana is five years older than Dalibor, but Dana is five years younger than Michael. Determine how old is Dana, Dalibor and Michael.
20. Elimination method
Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15

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