# Consecutive Multiples

• January 8th 2009, 08:01 AM
fecoupefe
Consecutive Multiples
John lists four consecutive multiples of some number. The average of the first two multiples is 28 and the average of the last two is 44. What is the greatest multiple on John's list?

Again, I'm stuck! Thanks for looking.
• January 8th 2009, 08:09 AM
Multiples
Hello fecoupefe
Quote:

Originally Posted by fecoupefe
John lists four consecutive multiples of some number. The average of the first two multiples is 28 and the average of the last two is 44. What is the greatest multiple on John's list?

Again, I'm stuck! Thanks for looking.

Suppose that the original number is $n$, and that the first multiple is $nr$. Then the next three multiples are $n(r+1)$, $n(r+2)$ and $n(r+3)$. So what you need to do is:

• Add together the first two multiples, and put the answer equal to $2 \times 28$
• Add together the last two multiples and put the answer equal to ...?

This will give you two equations for $n$ and $r$. Solve them to find the answers to your problem.