Question

The difference between two numbers is 8. If 2
is added to the greater number, the result will
be three times the smaller. Find the numbers.​

Answer 1

Answer:

★ Greater number = 13 ★

★ Smaller number = 5 ★

Step-by-step explanation:

Given:

• The difference between two numbers is 8.
• If 2 is added to the greater number, the result will be 3 times the smaller.

To find:

• The two numbers.

Solution:

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

According to the 1st condition,

• The difference between two numbers is 8.

$\implies$ x-y=8

$\implies$ x = 8+y................(i)

According to the 2nd condition,

• If 2 is added to the greater number, the result will be 3 times the smaller.

• If 2 is added to the greater number, the number will be = (x+2)

$\implies$ x+2=3y

• [ Put x = 8+y from eq(i) ]

$\implies$ 8+y+2=3y

$\implies$ y-3y=-10

$\implies$ -2y=-10

$\implies$ y = 10/2

$\implies$ y = 5

• Smaller number = 5

Now put y = 5 in eq(i) for getting the value of x.

x = 8+y

→ x = 8+5

→ x = 13

• Greater number = 13

__________________

Answer 2

$\large{\textbf{\underline{ \: Given:- \: \: }}}$

❏Diff. between two numbers is 8

❏After 2is added to the greater number the new number will be 3times the smaller one.

$\large{\textbf{\underline{ \: Find:- \: \: }}}$

❏What will be the numbers.

$\large{\textbf{\underline{ \: Solution:- \: \: }}}$

Let, the smaller number be x

and the greater number be y

☯$\underline{\textsf{According To Question:-}}$

$\sf \ast \: \: y - x = 8 ...... \bigg\langle eq....1\bigg\rangle$

$\sf \ast \: \: y + 2 = 3x ...... \bigg\langle eq....2\bigg\rangle$

Taking Eq. 1

$\sf \bullet\implies\: \: y - x = 8$

$\sf \bullet\implies\: \: y = 8 + x$

✪$\underline{\textsf{Using value of y in eq.1:-}}$

$\sf \dashrightarrow\: \: y + 2 = 3x$

$\sf \dashrightarrow\: \: 8 + x + 2 = 3x$

$\sf \dashrightarrow\: \: 10+ x= 3x$

$\sf \dashrightarrow\: \: 10= 3x - x$

$\sf \dashrightarrow\: \: 10=2x$

$\sf \dashrightarrow\: \: \dfrac{10}{2}=x$

$\sf \dashrightarrow\: \: 5=x$

$\therefore \underline{\textsf{\small{Smallest number, x = 5}}}$

✯$\underline{\textsf{Substituting the value of x in eq.1:-}}$

$\sf \implies\: \: y - x = 8$

$\sf \implies\: \: y - 5 = 8$

$\sf \implies\: \: y= 8 + 5$

$\sf \implies\: \: y= 13$

$\therefore \underline{\textsf{\small{Greater number, y = 13}}}$

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Hence,

• Smallest No. = 5
• Greatest No. = 13