Question

The sum of 5 consecutive odd number is 220.find the greatest of the 5 numbers.

Answer 1

Correct Question:

The sum of 5 consecutive even number is 220. Find the greatest of the 5 numbers.

Answer:

The greatest number is 48.

Step-by-step explanation:

Given

• The 5 numbers are odd consecutive.
• Sum of the numbers is 220

To Find

• The greatest number among the five.

Let first number = a

Second number = a + 2

Third number = a + 4

Forth number = a + 6

Fifth number = a + 8

According to the Question:

⟹ a + ( a + 2 ) + ( a + 4 ) + ( a + 6 ) + ( a + 8 ) = 220

⟹ a + a + 2 + a + 4 + a + 6 + a + 8 = 220

⟹ 5a + 2 + 4 + 6 + 8 = 220

⟹ 5a + 20 = 220

⟹ 5a = 220 - 20

⟹ 5a = 200

⟹ a = 200/5

⟹ a = 40

Fifth number = a + 8 = 40 + 8 = 48

The greatest number is 48.

Note: Sum of 5 odd numbers can not be an even number. So, there's no such five consecutive odd numbers exit whose sum is 220. So, I've answered it for even numbers.

Answer 2

Correct Question :-

• The sum of 5 consecutive even number is 220.find the greatest of the 5 numbers.

Given :-

• The sum of 5 Consecutive even number is 220.

To Find :-

• The Greatest of the 5 consecutive even number.

Solution :-

Let the First consecutive even number be x

Let the Second consecutive even number be x+2

Let the Third consecutive even number be x+4

Let the Fourth consecutive even number be x+6

Let the Fifth consecutive even number be x+8

According To Question :-

${:} \longrightarrow \sf{\sf{x \: + (x + 2) \: + (x + 4) \: + (x + 6) \: + (x + 8) \: = \: 220 }}$

${:} \longrightarrow \sf{\sf{x \: + x + 2 \: + x + 4 \: + x + 6\: + x + 8\: = \: 220 }}$

${:} \longrightarrow \sf{\sf{5x\: + \: 2 \: + \: 4 \: + 6 \: + \: 8 \: = \: 220 }}$

${:} \longrightarrow \sf{\sf{5x\: + \: 20\: = \: 220 }}$

${:} \longrightarrow \sf{\sf{5x\: = \: 220 \: - \: 20 }}$

${:} \longrightarrow \sf{\sf{5x\: = \: 200 }}$

${:} \longrightarrow \sf{\sf{x\: = \: \cancel\dfrac{200}{5} }}$

${:} \longrightarrow \sf{\bf{x\: = \: 40 }}$

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• First Number = x = 40
• Second Number = x + 2 = 40+2 = 42
• Third Number = x + 4 = 40 + 4 = 44
• Fourth Number = x + 6 = 40 + 6 = 46
• Fifth Number = x + 8 = 40 + 8 = 48

$\begin{gathered}\begin{gathered}\therefore\: \sf{ The \: Greatest \: number \: = \underline {\underline{ 48}}}\\\end{gathered}\end{gathered}$

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Verification :-

$\quad \longmapsto \sf \boxed{\bf{Sum \: of \: 5 \: consecutive \: number \: = \:220 }}$

$\quad \longmapsto \sf {\sf{ 40 \: + \: 42 \: + \: 44 \: + \: 46 \: + \: 48\: = \:220 }}$

$\quad \longmapsto \sf {\sf{ 126 \: + \: 94\: = \:220 }}$

$\quad \longmapsto \sf {\tt{ 220 \: = \:220 }}$

Hence, Proved

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