Question

The sum of 2 numbers is 80 and the greater number exceeds the smaller number by 11 . Find the numbers
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Answer 1

ㅤ$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• Sum of the 2 numbers is 80.

• The greater number exceeds the smaller number by 11.

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$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• What are the two numbers?

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$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

Let the greater number be x and the smaller number be y.

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Now,

A.T.Q

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• Sum of the 2 numbers is 80.

x + y = 80...........eq(1)

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• The greater number exceeds the smaller number by 11.

x = y + 11............eq(2)

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Substituting the value of x in eq(1)

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$\dashrightarrow \sf \: x + y = 80 \\ \\ \\\dashrightarrow \sf \: y + 11 + y = 80 \\ \\ \\ \dashrightarrow \sf \:2y = 80 - 11 \\ \\ \\ \dashrightarrow \sf \:2y = 69 \\ \\ \\ \dashrightarrow \sf \:y = \dfrac{69}{2} \\ \\ \\\dashrightarrow \sf \:{ \boxed{ \frak{ \purple{y = 34.5}}}}$

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Again, substitute the value of y in eqn(2).

$\dashrightarrow \sf \: x = y + 11 \\ \\ \\\dashrightarrow \sf \: x = 34.5 + 11 \\ \\ \\\dashrightarrow \sf \: { \boxed{ \frak{ \purple{x = 45.5}}}}$

ㅤ$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{ The greater and the smaller number will be \textbf{ 45.5 and 34.5 respectively }}}.$

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Answer 2

Answer:

lle us assume x and y are the two numbers and x>y

Given:x+y=80

Also given x=2y+11

substitute the values of x from the equation 1 in 2

2+11+y=80

3y+11=80

3y=80-11

3y=69

y=69 by 3 (division)

therefore:x=2y+11=(2*23)+11=57

The two numbers are 57 and 23

Explanation:

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