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Sum of two numbers is 29 and one number exceeds another by 5. Find the numbers.

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x = 12, y = 17

x = 14, y = 15

x = 12, y = 17

x = 12, y = 17

answer is A.

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Detailed Solution

Concept-
Let x be the lesser number.
Y will be the greater number.
The answer to the question

is 25,

which is the sum of two numbers.

\Rightarrow x + y = 29 — - (1)

Additionally, if one of the values is specified, then y is greater than z by 9.

\Rightarrow y = x + 5 —— (2)

Equation (1) is equal to

x + y = 29

when equation (2) is substituted.
(Adding variables)

x + x + 5 = 29 2 x + 5 = 29

(Rearranging so that constants are on the opposite side and variables are on one side.)

\Rightarrow 2 x = 29 - 5 \Rightarrow 2 x = 24 (Divide both side by 2)

\Rightarrow x = \frac{24}{2} \Rightarrow x = 12

We obtain the smaller number, and by substituting x in equation (2) to obtain the larger number, we have:
When replacing,

y = x + 5 y = 12 + 5 y = 17

By changing x and y in the equation, we can verify this response (1).
In other words,

12 + 17 = 29

12 + 17 = 29

29 = 29

that we have discovered the right solution.
The right response is thus

"x = 12, y = 17 . "

Hence, option 1 is correct.
ExamType: CBSE

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