The product of two consecutive positive multiples of 3 is 270. Which are these multiples?
Answer and explanation
Correct answer: 15 and 18
Let the smaller multiple be \(x\); then the next consecutive multiple is \(x+3\). Thus, \(x(x+3)=270\), giving \(x^2+3x-270=0\). Factoring gives \((x-15)(x+18)=0\). Since the multiples are positive, \(x=15\), so the two multiples are 15 and 18. Exam tip: You can also quickly verify the options by multiplying each pair and checking which product equals 270.
Frequently asked questions
What is the correct answer to this question?
15 and 18
Why is this the correct answer?
Let the smaller multiple be \(x\); then the next consecutive multiple is \(x+3\). Thus, \(x(x+3)=270\), giving \(x^2+3x-270=0\). Factoring gives \((x-15)(x+18)=0\). Since the multiples are positive, \(x=15\), so the two multiples are 15 and 18. Exam tip: You can also quickly verify the options by multiplying each pair and checking which product equals 270.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
