Question

The sum of two numbers is 97. If the greater number is divided by the smaller, the quotient is 7 and the remainder is 1. Find the numbers.​

Answer 1

Answer:

Smaller number = 12

Greater number = 85

Step-by-step explanation:

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

Given that:

x+y = 97

and x = 7y + 1

put x = 7y in x + y = 87

Then, 8y + 1 = 97

8y = 96

y = 12

and x = 85

HOPE IT'S RIGHT ANSWER

Answer 2

Given:

We're given with the sum of two numbers which is 97.

Need to find:

The smaller & greater number.

Solution: Let the greater number be x and the smaller number be y respectively.

Sum of both the given numbers is 97.

Therefore,

$:\implies\sf x + y = 97 \\\\:\implies\sf x = 97 - y\qquad\bigg\lgroup\bf Equation\;(I)\bigg\rgroup$

Also,

When the greater number is divided by the smaller number the Quotient is 7 and the remainder is 1.

Therefore, it can be written as:

⠀

$:\implies\sf x = 7y + 1\qquad\bigg\lgroup\bf Equation\;(II)\bigg\rgroup$

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{Putting\: value \; of \; x \; in \; Eq(2)\: :}}$⠀⠀⠀⠀

⠀

$:\implies\sf 97 - y = 7y + 1 \\\\\\:\implies\sf 97 - 1 = 7y + y \\\\\\:\implies\sf 96 = 8y \\\\\\:\implies\sf y = \cancel\dfrac{96}{8} \\\\\\:\implies{\underline{\boxed{\frak{\pink{y = 12}}}}}\;\bigstar$

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{From \; equation(1)\: :}}$⠀⠀⠀

⠀

$:\implies\sf x = 97 - y \\\\\\:\implies\sf x = 97 - 12 \\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 85}}}}}\;\bigstar$

⠀

$\therefore{\underline{\sf{Hence, \; the \; required\; numbers \; are \; \bf{12\; \&\; 85 }.}}}$

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: Verification \: :}}}}}\mid}$

Given that, sum of two numbers is 97.

⠀⠀⠀

Therefore,

⠀⠀⠀

$\dashrightarrow\sf x + y = 97 \\\\\\\dashrightarrow\sf 85 + 12 = 97 \\\\\\\dashrightarrow\sf 97 = 97$

⠀⠀⠀⠀⠀⠀⠀⠀$\therefore$ Hence Verified! ⠀⠀⠀⠀⠀

Answer 3

Given:

We're given with the sum of two numbers which is 97.

Need to find:

The smaller & greater number.

Solution: Let the greater number be x and the smaller number be y respectively.

Sum of both the given numbers is 97.

Therefore,

$:\implies\sf x + y = 97 \\\\:\implies\sf x = 97 - y\qquad\bigg\lgroup\bf Equation\;(I)\bigg\rgroup$

Also,

When the greater number is divided by the smaller number the Quotient is 7 and the remainder is 1.

Therefore, it can be written as:

⠀

$:\implies\sf x = 7y + 1\qquad\bigg\lgroup\bf Equation\;(II)\bigg\rgroup$

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{Putting\: value \; of \; x \; in \; Eq(2)\: :}}$⠀⠀⠀⠀

⠀

$:\implies\sf 97 - y = 7y + 1 \\\\\\:\implies\sf 97 - 1 = 7y + y \\\\\\:\implies\sf 96 = 8y \\\\\\:\implies\sf y = \cancel\dfrac{96}{8} \\\\\\:\implies{\underline{\boxed{\frak{\pink{y = 12}}}}}\;\bigstar$

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{From \; equation(1)\: :}}$⠀⠀⠀

⠀

$:\implies\sf x = 97 - y \\\\\\:\implies\sf x = 97 - 12 \\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 85}}}}}\;\bigstar$

⠀

$\therefore{\underline{\sf{Hence, \; the \; required\; numbers \; are \; \bf{12\; \&\; 85 }.}}}$

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: Verification \: :}}}}}\mid}$

Given that, sum of two numbers is 97.

⠀⠀⠀

Therefore,

⠀⠀⠀

$\dashrightarrow\sf x + y = 97 \\\\\\\dashrightarrow\sf 85 + 12 = 97 \\\\\\\dashrightarrow\sf 97 = 97$

⠀⠀⠀⠀⠀⠀⠀⠀$\therefore$ Hence Verified! ⠀⠀⠀⠀⠀

Answer 4

Given:

We're given with the sum of two numbers which is 97.

Need to find:

The smaller & greater number.

Solution: Let the greater number be x and the smaller number be y respectively.

Sum of both the given numbers is 97.

Therefore,

$:\implies\sf x + y = 97 \\\\:\implies\sf x = 97 - y\qquad\bigg\lgroup\bf Equation\;(I)\bigg\rgroup$

Also,

When the greater number is divided by the smaller number the Quotient is 7 and the remainder is 1.

Therefore, it can be written as:

⠀

$:\implies\sf x = 7y + 1\qquad\bigg\lgroup\bf Equation\;(II)\bigg\rgroup$

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{Putting\: value \; of \; x \; in \; Eq(2)\: :}}$⠀⠀⠀⠀

⠀

$:\implies\sf 97 - y = 7y + 1 \\\\\\:\implies\sf 97 - 1 = 7y + y \\\\\\:\implies\sf 96 = 8y \\\\\\:\implies\sf y = \cancel\dfrac{96}{8} \\\\\\:\implies{\underline{\boxed{\frak{\pink{y = 12}}}}}\;\bigstar$

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{From \; equation(1)\: :}}$⠀⠀⠀

⠀

$:\implies\sf x = 97 - y \\\\\\:\implies\sf x = 97 - 12 \\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 85}}}}}\;\bigstar$

⠀

$\therefore{\underline{\sf{Hence, \; the \; required\; numbers \; are \; \bf{12\; \&\; 85 }.}}}$

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: Verification \: :}}}}}\mid}$

Given that, sum of two numbers is 97.

⠀⠀⠀

Therefore,

⠀⠀⠀

$\dashrightarrow\sf x + y = 97 \\\\\\\dashrightarrow\sf 85 + 12 = 97 \\\\\\\dashrightarrow\sf 97 = 97$

⠀⠀⠀⠀⠀⠀⠀⠀$\therefore$ Hence Verified! ⠀⠀⠀⠀⠀

Answer 5

Given:

We're given with the sum of two numbers which is 97.

Need to find:

The smaller & greater number.

Solution: Let the greater number be x and the smaller number be y respectively.

Sum of both the given numbers is 97.

Therefore,

$:\implies\sf x + y = 97 \\\\:\implies\sf x = 97 - y\qquad\bigg\lgroup\bf Equation\;(I)\bigg\rgroup$

Also,

When the greater number is divided by the smaller number the Quotient is 7 and the remainder is 1.

Therefore, it can be written as:

⠀

$:\implies\sf x = 7y + 1\qquad\bigg\lgroup\bf Equation\;(II)\bigg\rgroup$

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{Putting\: value \; of \; x \; in \; Eq(2)\: :}}$⠀⠀⠀⠀

⠀

$:\implies\sf 97 - y = 7y + 1 \\\\\\:\implies\sf 97 - 1 = 7y + y \\\\\\:\implies\sf 96 = 8y \\\\\\:\implies\sf y = \cancel\dfrac{96}{8} \\\\\\:\implies{\underline{\boxed{\frak{\pink{y = 12}}}}}\;\bigstar$

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{From \; equation(1)\: :}}$⠀⠀⠀

⠀

$:\implies\sf x = 97 - y \\\\\\:\implies\sf x = 97 - 12 \\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 85}}}}}\;\bigstar$

⠀

$\therefore{\underline{\sf{Hence, \; the \; required\; numbers \; are \; \bf{12\; \&\; 85 }.}}}$

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: Verification \: :}}}}}\mid}$

Given that, sum of two numbers is 97.

⠀⠀⠀

Therefore,

⠀⠀⠀

$\dashrightarrow\sf x + y = 97 \\\\\\\dashrightarrow\sf 85 + 12 = 97 \\\\\\\dashrightarrow\sf 97 = 97$

⠀⠀⠀⠀⠀⠀⠀⠀$\therefore$ Hence Verified! ⠀⠀⠀⠀⠀