# Algebra - problems - page 54

1. Positive number z Positive number z is 10% greater than the number y. How many % is y smaller than z? Report the result rounded to one decimal place.
2. LCM Common multiple of three numbers is 3276. One number is in this number 63 times, second 7 times, third 9 times. What are the numbers?
3. Mom and daughter Mother is 39 years old. Her daughter is 15 years. For many years will mother be four times older than the daughter?
4. Star equation Write digits instead of stars so that the sum of the written digits is odd and is true equality: 42 · ∗8 = 2 ∗∗∗
5. One-third A one-third of unknown number is equal to five times as great as the difference of the same unknown number and number 28. Determine the unknown number.
6. Internal angles One internal angle of the triangle JAR is 25 degrees. The difference is the size of the two other is 15°. Identify the size of these angles.
7. Two rulers We have two rulers. Scale interval on first rulers are a spaced 1 cm and on second spaced 15 mm. Rulers are attached to each other so that they match initial divider commas. What next dividers commas coincide? Find at least three cases.
8. Store Peter paid in store 3 euros more than half the amount that was on arrival to the store. When he leave shop he left 10 euros. How many euros he had upon arrival to the store?
9. Rectangle The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
10. Collecting For the first week of material collection events are picked up at the school 850 kg of paper and 305 kg of rags which represented 55% of total collection for 14 days. How many kilograms of secondary raw materials were handed over totally?
11. Right triangle eq2 Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
12. Bridge piers One quarter of the bridge pier is sunk into the ground. Two thirds are in the water. Protruding above the water is 1.20 m long. Determine the height of bridge piers.
13. Sweets We want to prepare 5 kg of sweets for 150 CZK. We will mix cheaper candy: 1 kg for 120 CZK and more expensive candy: 1 kg per 240 CZK. How much of this two types of candy is necessary to prepare this mixture?
14. Rectangle - sides 4 Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5.
15. Unknown number 10 Number first increased by 30%, then by 1/5. What percentage we've increased the original number?
16. Pet store In a pet store, they are selling out the fish from one aquarium. Ondra wanted half of all fish, but they don't wish cut by hal fany fish he got one more than demanded. Matthew wished the remaining half of the fish, but as Andrew got half the fish more th
17. Steamer At 6 hours 40 minutes steamer sailed from the port at speed 12 km/h. At exactly 10 hours started sail motorboat at speed 42 km/h. When motorboat will catch steamer?
18. Divisibility by 12 Replace the letters A and B by digits so that the resulting number x is divisible by twelve /find all options/. x = 2A3B How many are the overall solutions?
19. AS sequence In an arithmetic sequence is given the difference d = -3 and a71 = 455. a) Determine the value of a62 b) Determine the sum of 71 members.
20. Divide Divide substance 110 cm long to two parts so that it first part is 10 cm longer than the second part and one part will be 10 times longer than the second portion. How long the parts will be?

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