Question

Deb and Ananya bought 20 toys together. From these 20 toys, Deb lost 3 toys and Ananya lost 4 toys. Product of the current number of their toys is 42. Can you form an equation for Deb to know how many toys did he have initially? [Let us assume Deb initially had x number of toys.]

Answer 1

$Total \: number \: of \: toys \: Deb \: and \\Ananya \: bought = 20$

$Let \: us \: assume \: number \: of \: toys \\Deb \: bought = x$

$Number \: of \: toys \: Ananya \: bought\\ = (20-x)$

$Number \: of \:toys\: Deb \: lost= 3$

$Number \: of \: toys \:Ananya \: lost = 4$

$Number \: of \: toys \: Deb \: have = ( x - 3 )$

$Number \: of \: toys \:Ananya \: have\\ = (20- x - 4 )\\= (16 - x)$

$Product \: of \: the \: current \: number \\of \: their \: toys = 42$

$\pink{ \implies ( x - 3 )( 16 - x ) = 42}$

$\implies 16x - x^{2} - 48 + 3x = 42$

$\implies 19x - x^{2} - 48 = 42$

$\implies 0 = x^{2} - 19x + 48 + 42$

$\implies x^{2} - 19x + 90 = 0$

/* Splitting the middle term, we get */

$\implies x^{2} - 10x - 9x + 90 = 0$

$\implies x( x - 10 ) - 9( x - 10 ) = 0$

$\implies ( x - 10 )( x - 9 ) = 0$

$\implies x - 10 = 0 \: Or \: x - 9 = 0$

$\implies x = 10 \: Or \: x = 9$

Therefore.,

Case 1:

$If \: x = 10$

$number \: of \: toys \:Deb \: bought = x = 10$

$number \: of \: toys \:Ananaya \: bought \\= 20 - x \\= 20 - 10 \\= 10$

Case 2:

$If \: x = 9$

$number \: of \: toys \:Deb \: bought = x = 9$

$number \: of \: toys \:Ananaya \: bought \\= 20 - x \\= 20 - 9 \\= 11$

•••♪

Answer 2

Step-by-step explanation:

$i \: hope \: its \: help \: uh$