Rearrange variables - practice problems - page 3 of 145
To isolate a variable in a formula, use inverse operations to systematically undo surrounding mathematical operations. For example, in 2x + 3 = 7 , subtract 3 from both sides ( 2x = 4 ), then divide by 2 ( x = 2 ). Maintain balance by applying each operation to both sides of the equation. For complex formulas, follow the order of operations (PEMDAS/BODMAS) in reverse, handling addition/subtraction before multiplication/division.Number of problems found: 2890
- Two cubes 2
Two cubes each of volume 125 cm³ are joined end to end. Find the surface area of the resulting cuboid . - Repeating to infinity
How do I express 0.99999999… as a fraction? (nine repeating) Another questions: Can you write .9999 repeating as a fraction? How do you turn 0.9 repeating into a fraction? - Angle of elevation
From a point A on the ground, the angle of elevation of the top of a 20 m tall of a building is 45°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from A is 60°. Find the length of the flagstaff and th - A long train
A train passes a standing man in 6 sec and 210 m long platform in 16 s . Find the length and the speed of the train. - Antecedent and consequent
In a ratio which is equal to 5:8, if the antecedent is 40, then find the consequent. - Direct proportional If m is proportional to n and m=5 when n=4, then what is the value of m when n=18?
- Two circles 3
Two circles are inscribed in a square whose side is 4 cm. Find the radius of the smaller circle. - The radius 3
The radius of a solid circular cylinder decreases by 20% and its height increases by 10% . Find the percentage change its : (a) volume (b) curved surface area. - Common work
39 men can repair a road in 12 days working 5 hours a day. How many days will be required to complete the work by 30 men working 6 hours a day? - Palidrom
A number consists of two digits whose product is 24. When 18 is subtracted from the number, the digits change their places. Find the number. - Long train
A 110 m long train crosses a tree in 3 s. How long will it take to cross a 165 m long platform and 135 m long bridge, If the platform and bridge are at a distance of 30 m? - Two men 2
Two men are on opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30° and 45°, respectively. If the height of the tower is 50 m, find the distance between the two men. - Square lawn
A square lawn has a 2 m wide path surrounding it. If the area of the path is 136 square meters, find the area of the lawn. - Three cubes
Three cubes of iron whose edges are 6 cm, 8 cm, and 10 cm, respectively, are melted and formed into a single cube. Find the edge of the new cube. - A town 3
A town with 12,000 people has been growing at a rate of 2.5% per year. How many years ago was the population 8,000? - An iron rod
If 22.5 meters of a uniform iron rod weighs 85.5 kg, what will the length of 22.8 kilograms of the same rod? - A sum 6
A sum at simple interest of 4% per annum amounts to 3120 USD in 5 years. Find the sum. - Move the average
If the average of 5 numbers is 20, the number which should be added to first number to make the average becomes 30? - South and then east
William walks 16 m south from his house and turns east to walk 63 m to reach his friend's house. While returning, he walks diagonally from his friend's house to reach back to his house. What distance did he walk while returning? - Average age 4 The average age of 31 people in a group is 19. If one person is reduced to 18, the average age becomes 18. Find the age of the reducing person.
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