Q2. A farmer has chickens and cows. If there are 20 heads and 56 legs in total, how many cows are there?
Solution:
Let the number of chickens be c and the number of cows be k. We have the equations: c + k = 20 and 2c + 4k = 56. Solving these gives k = 10.
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Q3. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer paid $70, how many miles did they drive?
Solution:
Let the number of miles driven be m. The total cost is given by: 50 + 0.20m = 70. Solving for m gives 0.20m = 20, so m = 100 miles.
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Q4. Solve for x: 2x - 4 = 10.
Solution:
2x - 4 = 10. Add 4 to both sides: 2x = 14. Divide by 2: x = 7.
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Q5. If 5x + 2y = 20 and y = 2, what is the value of x?
Solution:
Substitute y = 2 into 5x + 2(2) = 20. This gives 5x + 4 = 20. Subtract 4: 5x = 16. Divide by 5: x = 16/5 = 3.2.
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Q6. Solve for y: 2y - 4 = 10.
Solution:
2y - 4 = 10. Add 4 to both sides: 2y = 14. Divide by 2: y = 7.
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Q7. If 5 times a number decreased by 3 equals 12, what is the number?
Solution:
Let the number be x. The equation is: 5x - 3 = 12. Adding 3 to both sides gives 5x = 15, so x = 3.
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Q8. A train travels 60 km at a certain speed and returns at 90 km/h. If the total time for the journey is 4 hours, what is the speed of the train on the way to the destination?
Solution:
Let the speed of the train on the way to the destination be x km/h. The time taken to travel to the destination is 60/x hours and the time taken to return is 60/90 hours. The total time is given by: 60/x + 60/90 = 4. Solving for x gives x = 40 km/h.
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Q9. What is the solution to the inequality 2x + 5 > 15?
Solution:
2x + 5 > 15. Subtract 5 from both sides: 2x > 10. Divide by 2: x > 5.
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Q10. If a rectangle has a length of 3x and a width of 2x, what is its area?
