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This essential trains for: SAT-I, GMAT, AMC-8, Math Kangaroo 5-6, Math Kangaroo 7-8.

Summary

If a unit costs D dollars, the total to pay for N units is:

equation

The commission that a salesperson earns is generally paid by the seller.

The table summarizes the relations between cost, commission, sales tax:

Sticker price: D equation Professor Lidenbrock bought 45 ft.of gauge 1/4'' rope at 0.8 krona per foot and twice as much gauge 1/2'' rope at 1.5 krona per foot. How much was he quoted for the rope? equation

equation

equation
Sales commission: c% equation Based on the above quote, if Gunnar the salesperson was paid a 4% commission, how many kronas did he receive? equation
Seller receives: S equation Based on the quoted price and the sales commission, what is the net amount received by the seller "Gunnbjorns Fjeld Outfitters"? equation
Sales tax: t% equation If the Icelandic government charges 12% sales tax, what is the amount Professor Lidenbrock actually paid? equation

(Professor Lidenbrock is a character from Jules Verne's "Voyage to the Center of the Earth.")

Discount: After a discount of 25% a pair of tickets for a blimp ride costs only $300. What is the price of a ticket without the discount?

Denote the regular price of the pair of tickets with x. 300 dollars represents only 75% of the regular price:

equation

equation

equation

The price of a single ticket is:

equation

Markup: After all its competitors went out of business, Solocast marked up all its packages by 10%. Now, a valued customer pays $3.59 more for a basic package. What is the price of a basic package?

Denote the old price by x. 10% of the old price represents the amount the price was marked up by:

equation

The old price was:

equation

The new price is:

equation