Mathematics: Abookstore can purchase several calculators for a total cost of $120. if each calculators cost $1 less, the bookstore could purchase 10 additional calculators at the same total cost. how many calculators can be purchased at the regular price? how do i put this into an equation that i can solve?

Abookstore can purchase several calculators for

Ответ:

angelinaavila06

31.12.2021

$x-number\ of\ calculators\ sold\ in\ regular\ price\\\\
y-\ \ first\ price\\\\
(y-1)\ \ -second\ price\\\\x=\frac{120}{y}\\
x+10=\frac{120}{y-1}\\\\Substitude\ x=\frac{120}{y}\ into\ the\ second\\\\\
\frac{120}{y}+10=\frac{120}{y-1}\ \ |-\frac{120}{y-1}-10\\\\
\frac{120}{y}-\frac{120}{y-1}=-10\\\\Make\ a\ common\ denominator\\\\
\frac{120(y-1)}{y(y-1)}-\frac{120y}{(y-1)y}=-10
\frac{120y-120)}{y(y-1)}-\frac{120y}{(y-1)y}=-10\\\\
\frac{120y-120-120y}{y(y-1)}=-10$ $Assumptions:\\y \neq 0\ \ \ and\ \ y \neq 1\\\\ \frac{-120}{y(y-1)}=-10\ \ \ | *y(y-1) \\\\
-120=-10y(y-1)\\\\
-120=-10y^2+10y\\\\
10y^2-10y-120=0\ \ \ |:10\\\\
y^2-y-12=0\\\\Factor\ equation\\\\ y^2+3y-4y-12=0\\\\
(y-4)(y+3)=0\\\\Solutions:\ \ y=4\ \ and\ \ y=-3$