Question

QUESTIONS :-
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▪️The sum of three consecutive odd no is 87 . Find the numbers ?

▪️The sum of two numbers is 80 . If the larger number exceeds four times the smaller by 5 , what is the smaller number ?
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NOTE :- Spammer's Stay Away.
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& Show Explanation also in answer . ​

Answer 1

Question: 1) The sum of three consecutive odd no is 87 . Find the numbers?

Solution:

❒ Let the three consecutive odd numbers are x, (x + 2) and (x + 4).

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$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\bigstar\: According\: to \; the\; Question \: :}}}}\mid}$

• The sum of three consecutive odd no is 87.

$:\implies\sf x + x + 2 + x + 4 = 87 \\\\\\:\implies\sf 3x + 6 = 87\\\\\\:\implies\sf 3x = 87 - 6\\\\\\:\implies\sf 3x = 81 \\\\\\:\implies\sf x = \cancel\dfrac{81}{3}\\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 27}}}}}\;\bigstar$

❒ Hence, three consecutive odd numbers are:

• First number, x = 27

• Second number, (x + 2) = 27 + 2 = 29

• Third number, (x + 4) = 27 + 4 = 31

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$\therefore{\underline{\sf{Hence, \; three\: numbers\; are\; \bf{27,\:29,\;and\;31 }.}}}$

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Question: 2) The sum of two numbers is 80 . If the larger number exceeds four times the smaller by 5 , what is the smaller number?

Solution:

Given: The sum of two numbers is 80.

Need to find: The smaller number.

❒ Let the two numbers are x and y respectively.

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$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\bigstar\: According\: to \; the\; Question \: :}}}}\mid}$

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• The sum of two numbers is 80.

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$:\implies\sf (x + y) = 80$

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• If the larger number exceeds four times the smaller by 5.

Therefore,

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$:\implies\sf x = 4y - 5$

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$:\implies\sf 80 - y = 4y - 5 \\\\\\:\implies\sf 4y + y = 80 + 5 \\\\\\:\implies\sf 5y = 85 \\\\\\:\implies\sf y = \cancel\dfrac{85}{5}\\\\\\:\implies{\underline{\boxed{\frak{\pink{y = 17}}}}}\;\bigstar$

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Also,

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$:\implies\sf x = 4y - 5\\\\\\:\implies\sf x = 4(17) - 5 \\\\\\:\implies\sf x = 68 - 5\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 63}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence,\:the\: smaller\; number\;is\; \bf{17 }.}}}$

Answer 2

Qᴜᴇsᴛɪᴏɴ : 1

The sum of three consecutive odd no. is 87 . Find the numbers ?

Aɴsᴡᴇʀ :

Gɪᴠᴇɴ :

• The sum of three consecutive odd no is 87.

Tᴏ Fɪɴᴅ :

• The numbers.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

Let,

• The three consecutive odd numbers are x, (x + 2), (x + 3).

According to the question,

$\red\bigstar\:\bigg\{\:\bf\purple{x\:+\:(x\:+\:2)\:+\:(x\:+\:4)\:=\:87\:}\:\bigg\}\:\red\bigstar$

➙ $\:\bf{x\:+\:x\:+\:2\:+\:x\:+\:4\:=\:87\:}$

➙ $\:\bf{3x\:+\:6\:=\:87\:}$

➙ $\:\bf{3x\:=\:87\:-\:6}$

➙ $\:\bf{3x\:=\:81}$

➙ $\:\bf{x\:=\:\dfrac{81}{3}}$

➙ $\:\bf\blue{x\:=\:27}$

Hence,

✯ Three consecutive odd numbers are,

➻ x = 27

➛ (x + 2) = 27 + 2 = 29

➙ (x + 4) = 27 + 4 = 31

$\Large\tt{Therefore,}$

The three consecutive numbers are 27, 29 & 31.

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Qᴜᴇsᴛɪᴏɴ : 2

️The sum of two numbers is 80. If the larger number exceeds four times the smaller by 5 , what is the smaller number ?

Aɴsᴡᴇʀ :

Let,

• The larger number be x.

• And the smaller number be y.

Gɪᴠᴇɴ :

• ️The sum of two numbers is 80.

$\longmapsto\:\:\bf{x\:+\:y\:=\:80\:}---(i)$

• Larger number exceeds 4 times the smaller number by 5.

$\longmapsto\:\:\bf{x\:=\:4y\:-\:5}$

Tᴏ Fɪɴᴅ :

• The smaller number.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

↝ Putting the value of 'x' in equation (i), we get

➣ $\:\bf{(4y\:-\:5)\:+\:y\:=\:80\:}$

➣ $\:\bf{4y\:-\:5\:+\:y\:=\:80\:}$

➣ $\:\bf{5y\:=\:80\:+\:5}$

➣ $\:\bf{5y\:=\:85}$

➣ $\:\bf{y\:=\:\dfrac{85}{5}}$

➣ $\:\bf\pink{y\:=\:17}$

$\Large\tt{Therefore,}$

The smaller number is 17.