A worker completes 736 units of work in x days by doing x + 9 units daily. What is the number of days?
Answer and explanation
Correct answer: 23
Total work equals number of days multiplied by work completed per day. Therefore x(x + 9) = 736, giving x² + 9x − 736 = 0. The expression factors as (x − 23)(x + 32) = 0, so x = 23 or x = −32. A number of days cannot be negative, hence x = 23 is the valid solution. The daily output is then x + 9 = 32 units, and 23 × 32 = 736 confirms the result. Thus option B is correct. Option D is the daily work amount, not the number of days. Options A and C fail the product condition and do not give the stated total work.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
Total work equals number of days multiplied by work completed per day. Therefore x(x + 9) = 736, giving x² + 9x − 736 = 0. The expression factors as (x − 23)(x + 32) = 0, so x = 23 or x = −32. A number of days cannot be negative, hence x = 23 is the valid solution. The daily output is then x + 9 = 32 units, and 23 × 32 = 736 confirms the result. Thus option B is correct. Option D is the daily work amount, not the number of days. Options A and C fail the product condition and do not give the stated total work.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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