# System of equations - problems

- The sides

The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it. - Alice

Alice spent 5/11 of her money on a back pack. She has $42 dollars left. How much was her back pack? - Soaps

Each box has the same number of soaps. A quarter of all boxes contain only white soaps, and in each of the remaining 120 boxes there are always half the white soaps and half the green. White soaps total 1200. (a) the number of all soap boxes; (b) the sma - Two equations

Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5 - Largest angle of the triangle

Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - A bridge

A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H - A candle

A candle shop sells scented candles for $16 each and unscented candles for $10 each. The shop sells 28 candles today and makes $400. a. Write a system of linear equations that represents the situation. b. Solve the system to answer the questions: How m - Father 7

Father is 6 times older than his son. After 4 years, the father will only be 4 times older. What are their present ages? - 12 apples

12 apples and 2 loaves of bread cost 5.76 and 6 apples and 3 loaves of bread cost 7.68. How much is a loaf of bread? - 13 tickets

A short and long sightseeing tour is possible at the castle. Ticket for a short sightseeing circuit costs CZK 60, for a long touring circuit costs CZK 100. So far, 13 tickets have been sold for 1140 CZK. How much did you pay for tickets for a short tour? - Three points 2

The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D. - Perimeter of a rectangle

If the perimeter of a rectangle is 114 meters and the length is twice the width plus 6 meters, what are the length and width? - Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side. - Pool

If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately? - Forestry workers

In the forest is employed 64 laborers planting trees in nurseries. For 8 hour work day would end job in 35 days. After 12 days, 20 laborers go forth. How many days is needed to complete a planting trees in nurseries by others, if they will work 9 hours a - Excavation

Mr. Billy calculated that excavation for a water connection dig for 12 days. His friend would take 10 days. Billy worked 3 days alone. Then his friend came to help and started on the other end. On what day since the beginning of excavation they met? - Store

One meter of the textile were discounted by 2 USD. Now 9 m of textile cost as before 8 m. Calculate the old and new price of 1 m of the textile. - Motion

If you go at speed 5.1 km/h, you come to the station 37 minutes after leaving train. If you go by bike to the station at speed 28 km/h, you come to the station 38 minutes before its departure. How far is the train station? - Coffee

In stock are three kinds of branded coffee prices: I. kind......6.9 USD/kg II. kind......8.1 USD/kg III. kind.....10 USD/kg Mixing these three species in the ratio 8:6:3 create a mixture. What will be the price of 1100 grams of this mixture? - Cuboid

Cuboid with edge a=23 cm and body diagonal u=41 cm has volume V=13248 cm^{3.}Calculate the length of the other edges.

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