Question

Please answer this question​

Answer 1

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$\color{blue}\large\underline{\underline{Answer:}}$

1.

$(x) + (x + 7) + (x + 14) = 5x - 7 \\ 3x + 21 = 5x - 7 \\ 21 + 7 = 5x - 3x \\ 28 = 2x \\ x = \frac{28}{2} \\ x = 14$

$\color{green}\large\underline{\underline{Multiples:}}$

x = 14

x + 7 = 14 + 7 = 21

x + 14 = 14 + 14 = 28

2.

$10x + y = 9 \\ 10y + 9 = 10x + y - 9 \\ 10y - y - 10x = - 9 - 9 \\ - 10x + 9y = - 18 \\ \\ 10x + y = 9 \: \: \: \: \:(a) \\ - 10x + 9y = - 18 \: \: \: \: \: \:(b) \\ \\ (a) + (b) \\ 10x + y - 10x + 9y = 9 - 18 \\ 10y = - 9 \\ y = \frac{ - 9}{10} \\ \\ put \: in \: (a) \\ \\ 10x - \frac{9}{10} = 9 \\ 10x = 9 + \frac{9}{10} = \frac{99}{10} \\ x = \frac{ \frac{99}{10} }{10} = \frac{99}{100} \\ \\ original \: no. = 10x + y \\ = 10( \frac{99}{100} ) - \frac{9}{10} = \frac{99}{10} - \frac{9}{10} \\ = \frac{90}{10} \\ = 9$

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Answer 2

1.

Let the three consecutive multiples of 7 be $\sf{x-7,\ x}$ and $\sf{x+7.}$

Sum of these three numbers is 7 less than five times the first number.

$\longrightarrow\sf{(x-7)+x+(x+7)=5(x-7)-7}$

$\longrightarrow\sf{x-7+x+x+7=5x-35-7}$

$\longrightarrow\sf{3x=5x-42}$

$\longrightarrow\sf{5x-3x=42}$

$\longrightarrow\sf{2x=42}$

$\longrightarrow\sf{x=\dfrac{42}{2}}$

$\longrightarrow\underline{\underline{\sf{x=21}}}$

$\longrightarrow\sf{\underline{\underline{x-7=14}}}$

$\longrightarrow\sf{\underline{\underline{x+7=28}}}$

Hence the three consecutive multiples are 14, 21 and 28.

2.

Let the tens digit of the number be $\sf{x,}$ then ones digit will be $\sf{9-x.}$

Then the two digit number becomes,

• $\sf{10x+(9-x)=9x+9}$

The number formed on reversing the digits becomes,

• $\sf{10(9-x)+x=90-9x}$

The new number is 9 less than the original number.

$\longrightarrow\sf{90-9x=(9x+9)-9}$

$\longrightarrow\sf{90-9x=9x+9-9}$

$\longrightarrow\sf{90-9x=9x}$

$\longrightarrow\sf{9x+9x=90}$

$\longrightarrow\sf{18x=90}$

$\longrightarrow\sf{x=\dfrac{90}{18}}$

$\longrightarrow\sf{x=5}$

The original number is,

$\longrightarrow\sf{9x+9=9\times5+9}$

$\longrightarrow\sf{9x+9=45+9}$

$\longrightarrow\underline{\underline{\sf{9x+9=54}}}$

Hence 54 is the original number.