Maizah bought a pair of pants and a briefcase at a department store. The sum of the prices before sales tax was $130.00. There was no sales tax on the pants and a 9% sales tax on the briefcase. The total Maizah paid, including the sales tax, was $136.75. What was the price, in dollars, of the pants?
To answer the question, you first need to define the variables. The question discusses the prices of a pair of pants and a briefcase and asks you to find the price of the pants.
So it is appropriate to let P be the price of the pants, in dollars, and to let B be the price of the briefcase, in dollars. Since the sum of the prices before sales tax was $130.00, the equation P + B = 130 is true. A sales tax of 9% was added to the price of the briefcase. Since 9% is equal to 0.09, the price of the briefcase with tax was B + 0.09B = 1.09B. There was no sales tax on the pants, and the total Maizah paid, including tax, was $136.75, so the equation P + 1.09B = 136.75 holds.
Now, you need to solve the system P + B = 130 P + 1.09B = 136.75
Subtracting the sides of the first equation from the corresponding sides of the second equation gives you (P + 1.09B) − (P + B) = 136.75 − 130, which simplifies to 0.09B = 6.75. Now you can divide each side of 0.09B = 6.75 by 6.75 0.09.
This gives you В = — = 75. This is the value of B, the price, in dollars, 0.09 of the briefcase. The question asks for the price, in dollars, of the pants, which is P. You can substitute 75 for B in the equation P + B = 130, which gives you P + 75 = 130, or P = 130 − 75 = 55, so the pants cost $55.
(Note that this example has no choices. It is a student-produced response question. On the SAT, you would grid your answer in the spaces provided on the answer sheet.)
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