165k views
2 votes
A bookstore can purchase several calculators for a total cost of $720. If each calculator 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?

1 Answer

3 votes

Given:

A bookstore can purchase several calculators for a total cost of $720

Let the number of calculators = x

And the cost of one calculator = y

So,


xy=720\rightarrow(1)

If each calculator costs $1 less, the bookstore could purchase 10 additional calculators at the same total cost.

so,


(y-1)(x+10)=720\rightarrow(2)

divide the equation (2) by equation (1)


\begin{gathered} ((y-1)(x+10))/(xy)=1 \\ (y-1)(x+10)=xy \\ xy+10y-x-10=xy \\ 10y-x-10=0 \\ x=10y-10\rightarrow(3) \end{gathered}

Substitute with x into equation (1) then solve for y:


\begin{gathered} y(10y-10)=720 \\ 10y^2-10y=720 \\ 10y^2-10y-720=0\rightarrow(/10) \\ y^2-y-72=0 \\ (y+8)(y-9)=0 \\ y+8=0\rightarrow y=-8 \\ y-9=0\rightarrow y=9 \end{gathered}

Substitute into equation (1) to find x:


x=(720)/(9)=80

So, the answer will be:

The number of calculators can be purchased at the regular price = 80

User Jrbalsano
by
6.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.