Answer the following questions in full.

Your furniture store pays $$55\mathrm{.}00$ each for office chairs after receiving a trade discount of $45\%.$

Calculate the MSRP of each office chair

Show your calculations and the formula used

You decide to purchase a new piece of heavy equipment for $$147,000\mathrm{.}00,$ which is $$53,000\mathrm{.}00$ off the regular price

Determine the discount rate?

Show your formula and the calculation used.

A retail dealership purchases some new Old Town canoes to stock in its stores. Examining the merchandising terms of the manufacturer, Old Town, the dealership notices that it would be eligible to receive a $35\%$ trade discount, $15\%$ volume discount, and $3\%$ loyalty discount. Because it is January and Old Town are out of season, Old Town offers a seasonal discount of $12\%$ for purchases made before January $30.$ If the MSRP for the Old Town canoe is $$24,799\mathrm{.}00$ and the dealership purchases this item on January $15.$

What price would it pay?

Show your formula and the calculation used.

If a company knows that its profits are $15\%$ of the selling price and expenses are $30\%$ of cost$.$

What is the cost of a laptop player that has a regular selling price of $$999\mathrm{.}99?$

Show your formula and the calculation used

Sports Inn Bowling Lanes has set a pricing objective to maintain a markup of $$10\mathrm{.}50$ on lane rentals. The cost of providing the rental is $$4\mathrm{.}00.$ Every day, $($Early$)$ bowlers before $5$ p$.$m$.$ pay half$-$full price while $($twilight$)$ bowlers after $5$ p$.$m$.$ pay full$-$ price equaling $$15\mathrm{.}00.$ Typically, $75\%$ of the bowlers are $$twilight$$ bowlers.

What regular price and sale price should Sports Inn set to meet its pricing objective?