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If the first number is increased by 7 and the second number is reduced by 6 times, the sum of these numbers is 29.
If the first number is reduced by 5 and the second number is increased 2 times, the difference between the second and first number is 9.
Find these numbers.

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Answer:

First number = 20

Second number = 12

Explanation:

Let the 1st number be x

Let the 2nd number be y

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Condition 1

[tex]\sf \rightarrow x + 7 + \dfrac{y}{6} = 29[/tex]

[tex]\rightarrow \sf x=-\dfrac{y}{6}+22[/tex]

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Condition 2

[tex]\rightarrow \sf 2y - (x - 5) = 9[/tex]

[tex]\rightarrow \sf x = 2y -4[/tex]

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Substitute equations

[tex]\rightarrow \sf -\dfrac{y}{6}+22 = 2y-4[/tex]

[tex]\rightarrow \sf y=12[/tex]

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Find value of 1st number

[tex]\rightarrow \sf x = 2y - 4[/tex]

[tex]\sf \rightarrow x = 2(12) - 4[/tex]

[tex]\rightarrow \sf x = 20[/tex]

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