Daily Regents: Functions and Multiplying Polynomials

I'll be reviewing a New York State Regents Exam Question every day from now until the Regents exams begin next month. At least, that is the plan.

August 2014, Questions 27 and 28

27. Guy and Jim work at a furniture store. Guy is paid $185 per week plus 3% of his total sales in dollars, x, which can be represented by g(x) = 185 + 0.03x. Jim is paid $275 per week plus 2.5% of his total sales in dollars, x, which can be represented by f(x) = 275 + 0.025x. Determine the value of x, in dollars, that will make their weekly pay the same.

To find the value of x where both functions are the same, you can set them each to each other, and solve the equation.

g(x) = f(x)
185 + 0.03x = 275 + 0.025x
185 + 0.005x = 275
0.005x = 90
x = 90/0.005 = 18,000

If they both have sales of $18,000, their salaries will be equal.

If you want to check, put 18,000 into each function. Both will give you $725.

28. Express the product of 2x² + 7x - 10 and x + 5 in standard form.

Use the Distributive Property. Then combine like terms, writing the terms starting with the highest exponent and going in descending order.

(x)(2x² + 7x - 10) + (5)(2x² + 7x - 10)
2x³ + 7x² - 10x + 10x² + 35x - 50
2x³ + 17x² + 25x - 50

Any questions?

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If anyone in Brooklyn is looking for an Algebra or Geometry Regents Prep tutor, send me a note. I have a couple of weekly spots available between now and June.