# 9th grade (14y) + system of equations - examples

- Digit sum

The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number? - Birthday

Mother bought 21 desserts on the occasion of Mirka's birthday one tips was 9 CZK and the kremlin cost 12 CZK. For all desserts, she paid 213 CZK. How many kremlins and how many tips mums did buy? - Highway tunnel

The highway tunnel was built from two ends in the north-south direction. The average daily performance of the "northern party" rasters was higher than the average daily power of the "southern party" of the rasters. After 55 business days, both parties met. - Two workers

Two workers should fulfill certain task together for 5 days. If the first worker increased their performance twice and second twice fell, it took them just four days. For how many days would handle the entire task first worker himself? - Two unknown numbers

One number is 2 less than a second number. Twice the second number is 14 less than 5 times the first. Find the two numbers. - T-shirts and hat

5 t-shirts and a hat cost £62.00 2 t-shirts and a hat cost £29.00 How much does a t-shirt cost ? How much does a hat cost ? - Substitution

solve equations by substitution: x+y= 11 y=5x-25 - Pool

If water flows into the pool by two inlets, fill the whole for 9 hours. First inlet filled pool 8 hour longer than second. How long pool is filled with two inlets separately? - Store

One meter of the textile were discounted by 2.4 USD. Now 6 m of textile cost as before 3 m. Calculate the old and new price of 1 m of the textile. - Cuboid

Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm^{3.}Calculate the length of the other edges. - Right triangle Alef

The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs. - Circle arc

Circle segment has a circumference of 13.26 mm and 252.03 mm^{2}area. Calculate the radius of the circle and size of central angle. - Triangle ABC

Calculate the sides of triangle ABC with area 883 cm^{2}and if a: b: c = 15:7:19 - Right triangle

Legs of right are in ratio a:b = 5:8. Hypotenuse has a length of 16 dm. Calculate the perimeter and area of the triangle. - Motion

Cyclist started at 5:00 from point N to point O. After 20 minutes, followed him at the same speed the second cyclist. Walker, which went from O to N, started at 5:40. After 56 minutes he met the first cyclist and after next 16 minutes the second cyclist. D - Gear

Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears? - Barrel of oil

Barrel of oil weighs 238 kg. When it mold 20% oil, weighed 196 kg. What is the mass of the empty barrel? - R triangle

Calculate the area of a right triangle whose longer leg is 9 mm shorter than the hypotenuse and 4 mm longer than the shorter leg. - Pedestrian up-down hill

Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian? - Medians

Calculate the sides of a right triangle if the length of the medians to the legs are t_{a}= 23 cm and t_{b}=14 cm.

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