# System of equations - math word problems

1. Sales of products
For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold?
2. Angles ratio
The internal angles of a triangle are in ratio 1:4:5 What kind of triangle is it? (solve internal angles and write down and discuss)
3. Trapezoid
How long are the trapezoid bases with area 24 cm2 and height 3 cm. One base is 3 times longer than the shorter.
4. Savings
Paul has a by half greater savings than half Stanley, but the same savings as Radek. Staney save 120 CZK less than Radek. What savings have 3 boys together?
5. Bags
The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights.
6. Electricity consumption cost
Last year Karol family reduced its electricity consumption by 31% compared to the previous year and paid CZK 2883 less. How many CZK is electricity last year and how many two year ago?
7. Have solution
The sum of four consecutive even numbers is 96. Determine these numbers.
8. Rectangle
Find the dimensions of the rectangle, whose perimeter is 108 cm and the length is 25% larger than the width.
9. 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?
10. Potatoes 6
The farmer brought potatoes to the market. In the first hour he sold two-fifths of the potatoes brought, in the second hour he sold five-sixth of the remaining potatoes, and in the third hour he had sold the last 40kg of potatoes. How many kg of potatoes
11. Benches
The park has 64 benches. Occupied are by 18 more than empty. How many benches are occupied and empty ?
12. Empty canister
The canister is filled with oil weight 17 kg. If filled only half weight 9 kg. What weight does my empty canister have?
13. Triangle ABC
In a triangle ABC side b measure 10 cm less than the side a and side b is half of the side c. Calculate the length of sides if the circumference of the triangle is 42 cm.
14. Parallelogram
Side a of parallelogram is twice longer than side b. Its circumference is 78 dm. Calculate the length of the sides of a parallelogram.
15. Comparing salaries
Spouses compared salaries. Mrs. Janka found that a 20% higher salary than Mr Jaroslav. Together earned € 1,430. How much they earn each of them?
16. Rectangle
The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
17. Two sisters
Two sisters together have 54 CDs. 6/8 CDs has younger sister and is equal to 3/5 of CDs older sisters. How many CDs has each of the sisters?
18. Body diagonal
The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
19. Father and sons
After15 years will father many years as his two sons together now. There is a six-year difference between the brothers, and the older one celebrated fifty years three years ago. How old is their father now?
20. Time gone
Square of Richard age equals the age of his mother. When he will bw two times older then his mom will be 7/2 times older than he. How old is Richard and his mom?

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