Question

an integer is divided by 4 and gives a remainder of 3. The resulting quotient is divided by 5 and gives a remainder of 2 the resulting quotient is then divided by 9 giving a quotient of 1 and the remainder of 7 find the number
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Answer 1

Answer:

The number is 331.

Step-by-step explanation:

let x be the first no divided by 4 and give t as quotient.

Let y be quotient when t is divided by 5

According to the Question,

By Division algorithm which states that

Dividend =  Divisor × Quotient + Remainder

x = 4t + 3 ................(1)

t = 5y + 2 ...............(2)

y = 9 × 1 + 7

⇒ y = 16

put value of y in (2),

t = 5 × 16 + 2

t = 82

Now, Put value of t in (1)

x = 4 × 82 + 3

x = 331

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Answer 2

${\mathtt{\red{Solution}}}$

We know about Euclid's division lemma :-

${\boxed{\mathtt{\blue{a \: = \: bq \: + \: r }}}}$

Let the integer as a ⇝

So when a is divided by 9 it gave quotient b and 3 as remainder .

Implying Euclid's division lemma here :-

⇝ a = 4(b) + 3 .......eq 1

Now here b is the quotient .

So, b will again divided by 5 , it leaves 2 as remainder and gave c as quotient .

⇝ b = 5(c) + 2 ........ eq 2

Now c is divided by 9 .

So, it gave 1 as quotient and leaves 7 as remainder .

⇝ c = 9(1) + 7

⇝ c = 9 + 7

⇝ ${\boxed{\boxed{\mathtt{C \:=\: 16}}}}$

Putting the value of C in eq 2

⇝ b = 5 ( c ) + 2

⇝ b = 5 ( 16) + 2

⇝ b = 80 + 2

⇝ ${\boxed{\boxed{\mathtt{b \:=\: 82}}}}$

Putting the value of b in eq 1

⇝ a = 4 ( b) + 3

⇝ a = 4(82) + 3

⇝ a = 328 + 3

⇝ ${\boxed{\boxed{\mathtt{a \: =\:331}}}}$

${\underline{\mathtt{\blue{So\: the\: required\: number\: is \: 331}}}}$