A student solves (x+4) questions each day for x days and solves 320 questions in total. What is the value of x?
Answer and explanation
Correct answer: 16
The total number of questions is x(x+4). Hence, x(x+4)=320, giving x²+4x−320=0. Factoring, (x+20)(x−16)=0, so x=−20 or x=16. Since the number of days cannot be negative, x=16 is valid. Exam tip: In word problems, calculate both roots of the quadratic and retain only the value that fits the real-world condition.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The total number of questions is x(x+4). Hence, x(x+4)=320, giving x²+4x−320=0. Factoring, (x+20)(x−16)=0, so x=−20 or x=16. Since the number of days cannot be negative, x=16 is valid. Exam tip: In word problems, calculate both roots of the quadratic and retain only the value that fits the real-world condition.
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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