Question

The number of shells in Box A was 12 more than in Box B. When 96 shells were transferred from Box A to Box B, the number of shells in Box B became 3 times that of Box A. Find the total number of shells in Box A at first.

Answer 1

Answer:

186

Step-by-step explanation:

Let their are x shells in box B, there must be 12 more = x + 12 shells in box A.

When 96 shells were transferred from A to B,

No. of shells in A = (x + 12) - 96 = x - 84

No. of shells in B = (x) + 96 = x + 96

As stated, now, no. of shells in box B became 3 times that of box A.

=> (x + 96) = 3(x - 84)

=> x + 96 = 3x - 252

=> 252 + 96 = 3x - x

=> 348 = 2x

=> 348/2 = 174 = x

Therefore, total no. of shells in box A = x + 12 = 174 + 12 = 186

Answer 2

❍ Let's say that the number of shells in Box B be a .

⠀⠀⠀⠀⠀⠀Given that ,

• The number of shells in Box A was 12 more than in Box B.

⠀Therefore,

⠀⠀⠀⠀➠ ⠀Number of shells in Box A will be : ( a + 12 ) .

⠀⠀⠀⠀⠀⠀⠀AND ,

• 96 shells were transferred from Box A to Box B .

⠀Therefore,

⠀⠀⠀⠀➠ Number of shells in Box A will be : ( x + 12 ) - 96 = ( a - 84 ) .

⠀⠀⠀⠀➠ Number of shells in Box B will be : ( a + 96 )

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:According \: to\: the \: Question \::}}$

⠀⠀⠀━━━When 96 shells were transferred from Box A to Box B, the number of shells in Box B became 3 times that of Box A.

$\qquad \dashrightarrow \sf \bigg(\:Shells \: in \:Box \:B_{( \: When \:96\:transfered \:)} \:\bigg)\:=\:3\:\bigg(\:Shells \: in \:Box \:A_{( \: When \:96\:transfered \:)} \bigg)\:$

$\qquad \dashrightarrow \sf \bigg(\:a + 96 \:\bigg)\:=\:3\:\bigg(\:a - 84\: \bigg)\:$

$\qquad \dashrightarrow \sf \bigg(\:a + 96 \:\bigg)\:=\:\:\bigg(\:3a - 252\: \bigg)\:$

$\qquad \dashrightarrow \sf \:a + 96 \:\:=\:\:\:3a - 252\: \:$

$\qquad \dashrightarrow \sf \:a + 96 + 252 \:\:=\:\:\:3a\: \:$

$\qquad \dashrightarrow \sf \:a + 348 \:\:=\:\:\:3a\: \:$

$\qquad \dashrightarrow \sf \:348 \:\:=\:\:\:3a-a\: \:$

$\qquad \dashrightarrow \sf \: 348 \:\:=\:\:\:2a\: \:$

$\qquad \dashrightarrow \sf \: \cancel {\dfrac{348}{2} }\:\:=\:\:\:a\: \:$

$\qquad \dashrightarrow \sf \: 174 \:\:=\:\:\:a\: \:$

$\qquad \therefore \:\:\pmb{\underline{\purple{\frak{\:\:a\: =\:174\: }}} }\:\bigstar$

Therefore,

• Numbers of shells in Box A is : a + 12 = 174 + 12 = 186 shells .
• Numbers of shells in Box B is : a = 174 shells

$\qquad \therefore \:\: \underline {\sf \: Hence, \; The \: Numbers \: of \: shells \: in \: Box \: A \: and \: B \: are \: \bf 174 \: and \: 186 \: \sf shells \:,\:respectively \:.}$