Question

Q8. The sum of two numbers is 20. If twice the first number x is 13 more

than second number y, frame the equations for the given statements.

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Answer 1

Given:-

▪ Sum of two numbers is 20.

▪ Twice the first number x is 13 more than second number y.

To Find :-

▪ Equations for the given condition

Solution :-

Let the numbers be x and y respectively.

According to the question,

Case 1 :-

☞ The Sum of the two numbers is 20

Numbers we assumed are x and y.

∴ x + y = 20 ...(1)

Case 2 :-

☞ Twice the number x is 13 more than y.

Numbers we assumed are x and y.

⇒ 2x = y + 13

⇒ 2x - y = 13 ...(2)

Hence, The equations for this given condition are,

• x + y = 20
• 2x - y = 13

Let us find the required numbers,

Adding (1) and (2),

⇒ x + y + 2x - y = 20 + 13

⇒ 3x = 33

⇒ x = 11

Substituting x = 11 in (1)

⇒ 11 + y = 20

⇒ y = 20 - 11

⇒ y = 9

Hence, The numbers are 11 and 9.

Answer 2

GIVEN :-

• Tʜᴇ sᴜᴍ ᴏғ ᴛᴡᴏ ɴᴜᴍʙᴇʀs ɪs 20 .

• Iғ ᴛᴡɪᴄᴇ ᴛʜᴇ ғɪʀsᴛ ɴᴜᴍʙᴇʀ ɪs 13 ᴍᴏʀᴇ ᴛʜᴀɴ sᴇᴄᴏɴᴅ ɴᴜᴍʙᴇʀ .

TO FIND :-

• Tʜᴇ ᴇǫᴜᴀᴛɪᴏɴ ғᴏʀ ᴛʜᴇ ɢɪᴠᴇɴ sᴛᴀᴛᴇᴍᴇɴᴛs .

SOLUTION :-

Let,

• First number be “x” .

• And second number be “y” .

According to the question,

Cᴀsᴇ - 1 :-

$\huge\orange\star$ x + ʏ = 20 ------(1)

Cᴀsᴇ - 2 :-

$\huge\green\star$ 2x = 13 + ʏ

➪ 2x - ʏ = 13 ------(2)

☯︎ Nᴏᴡ, ᴀᴅᴅɪɴɢ ᴇǫᴜᴀᴛɪᴏɴ(1) ᴀɴᴅ ᴇǫᴜᴀᴛɪᴏɴ(2)

➪ 2x - ʏ + x + ʏ = 13 + 20

➪ 3x = 33

➪ x = 33/3

➪ x = 11

$\rm\pink{\therefore}$ Tʜᴇ ғɪʀsᴛ ɴᴜᴍʙᴇʀ ɪs "11" .

☯︎ Pᴜᴛᴛɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ "x" ɪɴ ᴛʜᴇ ᴇǫᴜᴀᴛɪᴏɴ(1),

➪ 11 + ʏ = 20

➪ ʏ = 20 - 11

➪ ʏ = 9

$\rm\pink{\therefore}$ Tʜᴇ sᴇᴄᴏɴᴅ ɴᴜᴍʙᴇʀ ɪs "9" .