Question

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 ?​

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

The sum of three consecutive odd no is 87.

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

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

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

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Also,

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

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