Question

The sum of two numbers is 8. The sum of three times the smaller number
and twice the larger number is 18. Find the two numbers.​

Answer 1

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Let the two numbers be x and y.

According to question

x + y = 8 ------------(I)

3x + 2y = 18 -----------(ii)

equ. (I) is multiplied by 3 and equ. (ii) is multiplied by 1

x+y=8 × 3

3x +2y = 18 × 1

3x + 3y = 24

3x + 2y = 18

put y=6 in either of equ.

$\bf \: x + y = 8 \\ \\ \bf \dashrightarrow \: x + 6 = 8 \\ \\ \bf \dashrightarrow \: x = 8 - 6 \\ \\\bf \dashrightarrow \red{ x = 2}$

The largest no or y: 6

The smallest no. ot x = 2

The required no's are = 6 and 2

Answer 2

Answer:

The numbers are 6 and 2.

Step-by-step explanation:

Sum of the numbers = 8

So,

Let the numbers be x and y. (x > y)

According to the first condition:

⇒ x + y = 8

⇒ x = 8 - y ----- (Eq. 1)

Second condition:

The sum of three times the smaller number

and twice the larger number is 18.

⇒ 3(y) + 2(x) = 18

⇒ 3y + 2(8 - y) = 18 ----- (Substitute eq.1)

⇒ 3y + 16 - 2y = 18

⇒ 3y - 2y = 18 - 16

⇒ y = 2

Smaller number = 2

___________________

★ Another number:

⇒ x = (8 - y)

⇒ x = (8 - 2)

⇒ x = 6

The numbers = 6 and 2.

Therefore, the numbers are 6 and 2.