Question

The sum of two numbers exceeds thrice the smaller by 2. If the difference between them is 19, find the numbers.

Answer 1

ǫᴜᴇsᴛɪᴏɴ :-

The sum of two numbers exceeds thrice the smaller by 2. If the difference between them is 19.

ᴛᴏ ғɪɴᴅ :-

• Numbers

sᴏʟᴜᴛɪᴏɴ :-

Let the larger number be x & smaller number be y

then,

✞ According to 1st condition :-

➭ Larger no + Smaller no = 3×Smaller no + 2

➭ x + y = 3y + 2

➭ x = 3y - y + 2

➭ x = 2y + 2 ---(1)

✞ According to 2nd condition :-

➭ Larger no - Smaller no = 19

➭ x - y = 19

➭ x = 19 + y. ---(2)

From (1) & (2) , we get,

➭ 2y + 2 = 19 + y

➭ 2y - y = 19 - 2

➭ y = 17

Put y = 17 in (1) , we get

➭ x = 2y + 2

➭ x = 2×17 + 2

➭ x = 34 + 2

➭ x = 36

Hence,

• Larger number = x = 36
• Smaller number = y = 17

Answer 2

Answer:

Let the Greater Number be G and Smaller Number be S respectively.

Given : The sum of two numbers exceeds thrice the smaller by 2.

$:\implies\sf G + S = 3S+2\\\\\\:\implies\sf G=3S-S+2\\\\\\:\implies\sf G=2S+2\qquad... eq(l)$

$\rule{100}{0.8}$

Given : Difference between them is 19.

$:\implies\sf G-S=19$

☢ Putting the value of G from eq. ( I )

$:\implies\sf 2S+2-S=19\\\\\\:\implies\sf 2S-S=19-2\\\\\\:\implies\underline{\boxed{\sf S=17}}\qquad\bigg\lgroup\bf Smaller\: Number\bigg\rgroup$

⠀⠀$\rule{160}{1.5}$

☢ Putting the value of S from eq. ( I ) :

$:\implies\sf G=2S+2\\\\\\:\implies\sf G=2(17)+2\\\\\\:\implies\sf G=34+2\\\\\\:\implies\underline{\boxed{\sf G=36}}\qquad\bigg\lgroup\bf Greater\: Number\bigg\rgroup$