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The sum of three consecutive multiples of 8 is 2424, find the largest one.
824
848
810
816
816
Let the three consecutive multiples of 8 be x−8, x, and x+8. Their sum is 3x=2424, so x=32424=808. The largest multiple is x+8=816.
Sum of three consecutive multiples of 8 is 2424
x+(x+8)+(x+16)=2424
Let the three consecutive multiples of 8 be x−8, x, and x+8. Their sum is 3x=2424, so x=32424=808. The largest multiple is x+8=816.
Finding the middle number instead of the largest number or assuming the common difference is 1 instead of 8 for consecutive multiples.
Assume the numbers
Let the three consecutive multiples of 8 be represented as x, x+8, and x+16.
x,x+8,x+16
Set up the linear equation
According to the problem, the sum of these three numbers is 2424.
x+(x+8)+(x+16)=2424
Solve for x
Simplify and solve for x: 3x+24=2424⟹3x=2400⟹x=800. Wait, let's re-verify: 3x+24=2424⟹3x=2400⟹x=800. Let's check: 800+808+816=2424. Thus the numbers are 800, 808, 816.
x=800
Find the largest number
The largest number is x+16=800+16=816.
800+16=816
D is correct because the three consecutive multiples of 8 are 800, 808, and 816, and the largest one is 816.
For any set of n consecutive numbers or multiples with an odd count n, the average is always equal to the exact middle number, simplifying calculations immensely.
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