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Linear equations in one variable SAT question

Math · Algebra · Hard · Answer it here, explanation included.

Townsend Realty Group Investments
Property address	Purchase price (dollars)	Monthly rental price (dollars)
Clearwater Lane	128,000	950
Driftwood Drive	176,000	1,310
Edgemont Street	70,000	515
Glenview Street	140,000	1,040
Hamilton Circle	450,000	3,365

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations. Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?

ExplanationShow

Choice B is correct. Let x be the original price, in dollars, of the Glenview Street property. After the 40% discount, the price of the property became $0 point 6 x$ dollars, and after the additional 20% off the discounted price, the price of the property became $0 point 8 times 0 point 6 x$ . Thus, in terms of the original price of the property, x, the purchase price of the property is $0 point 4 8 x$ . It follows that $0 point 4 8 x equals 140,000$ . Solving this equation for x gives $x equals 291,666 point 6, with the 6 repeating after the decimal point$ . Therefore, of the given choices, $291,700 best approximates the original price of the Glenview Street property.

Choice A is incorrect because it is the result of dividing the purchase price of the property by 0.4, as though the purchase price were 40% of the original price. Choice C is incorrect because it is the closest to dividing the purchase price of the property by 0.6, as though the purchase price were 60% of the original price. Choice D is incorrect because it is the result of dividing the purchase price of the property by 0.8, as though the purchase price were 80% of the original price.

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