Isolating a variable in the formula - practice problems - page 2 of 44
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: 874
- A sum 6
A sum at simple interest of 4% per annum amounts to 3120 USD in 5 years. Find the sum. - 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. - Split 207
Split number 207 into three parts such that these are in the arithmetic progression (AP) and the product of two smaller parts is 4623. - Stocks and bonds
Mr. Cash invested $80000 in various stocks and bonds. He earned a 7% dividend on his stocks and 5% interest on his bonds, for a one year profit (both stocks and bonds) of $4,900. How much did Mr. cash invest in bonds?
- Work men and women Two men and 1 woman can do a piece of work in 14 days, while 4 women and 2 men can do the same work in 8 days. If a man get 90 euros/day, what should be the wages/day of a woman?
- Two trains 11
Two trains running in opposite direction cross a man standing on the platform in 27 seconds and 17 seconds and they cross each other in 23 seconds. Find the ratio of their speeds. - The speeds
The speeds of three cars are in the ratio 2:3:4. What is the ratio of the times taken by these cars to travel the same distance? - One combine
One combine harvester can harvest a field of corn in 4.5 hours. Another harvester can harvest the same field in 3 hrs. If the farmer uses the two harvesters at the same time. How long will it take to harvest the entire field? - A tank 2
A tank can be filled by a pipe A in 3 hours and by pipe B in 5 hours. When the tank is full, it can be drained by pipe C in 4 hours. If the tank is initially empty and all three pipes are open, how many hours will it take to fill up the tank?
- Consumption stable
If the price of sugar rises from Rs 6/kg to Rs 7.50/kg. A person having no increase in his expenditure on sugar, will have to reduce his consumption by? - The average 15 The average age of a group of four men whose ages are in the ratio of 2:3:4:5 is 42 years, what is the age of the eldest person of this group?
- Three Numbers GP
The sum of three Numbers in geometric progression (GP) is 38, and their product is 1728. Find the Numbers. - Height or altitude
Find the altitude (in cm) of side MT of triangle MNT with side MN = 36 cm, MT = 36 cm and NT = 48 cm. - Three workers
A can do a work in 16 hours, and B alone in 24 hours. If A, B, and C work together and finish it in 8 hours, then C alone can finish it in how many hours?
- A rectangle 14
A rectangle is 8 cm long and 5 cm wide. Its perimeter is doubled when each of its sides is increased by x cm. From an equation in x, find the new length of the rectangle. - The 5th The 5th, 8th and 11th terms of a GP are a, b, c respectively. Show that a, b, c are in GP.
- Parallel tracks
Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6 km/hr less than the faster one, its length, in - A pair 2 Jane is 5 years older than Tom. In 3 years, the sum of their ages will be 41. How old are Jane and Tom now?
- Circle inscribed square
What is the area of the circle that can be inscribed in a square of 10 cm?
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