Answer:
66
Step-by-step explanation:
11,22,33,44, and 55 are 5 consecutive multiples of 11.
11=11(1)
22=11(2)
33=11(3)
44=11(4)
55=11(5)
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You can see consecutive multiples of 11 where we don't know the actual multiples will look like:
11n,11(n+1),11(n+2),11(n+3),11(n+4).
Now we are given the sum of the numbers I just mentioned is 220.
This means,
11n+11(n+1)+11(n+2)+11(n+3)+11(n+4)=220
Each term 11n,11(n+1),11(n+2),11(n+3),11(n+4), and 220 all have a common factor of 11 so divide both sides by 11:
1n+1(n+1)+1(n+2)+1(n+3)+1(n+4)=20
1 times anything is still just that anything:
n+n+1+n+2+n+3+n+4=20
Combine the like terms:
n+n+n+n+n+1+2+3+4=20
Simplify the combining:
5n+10=20
Subtract 10 on both sides:
5n =10
Divide both sides by 5:
n =10/5
Simplify right hand side:
n =2
So if n=2, then the multiples of 11 in question look like this:
11n=11(2)=22
11(n+1)=11(3)=33
11(n+2)=11(4)=44
11(n+3)=11(5)=55
11(n+4)=11(6)=66
--------------------------Add up to see if sum is actually 220.
Putting into my calculator gives me a result of 220.
We are good.
Now you just have to determine what the greatest of the number 22,33,44,55, and 66 is...
The greatest listed here is 66.
