Claire went into a movie theater and bought 9 bags of popcorn and 2 pretzels, costing a total of $80. Melanie went into the same movie theater and bought 7 bags of popcorn and 4 pretzels, costing a total of $72. Write a system of equations that could be used to determine the price of each bag of popcorn and the price of each pretzel. Define the variables that you use to write the system.

More challenges: 1) factor out the indicated quantity.8mn² + 7mn - m : factor out the quantity -m2) factor the polynomial by grouping.2vw + 7cv + 14cw + 49c²3) factor completely using the difference of squares along with factoring by grouping.25v³ - 25v² - 4v + 44) factor the sum of cubes. 125x³ + 645) q³ + 27r³6) factor completely. use difference of squares.729p^6 - 6^67) solve the equation(7x + 4)(9x - 1) = 08) a. find the values of x for which f (x) = 0b. find f (0)f (x) = x² + 2x - 489) find the x and y-intercepts for the function defined by y = f (x)f (x) = (x + 3)(x + 4)(x - 1)²10) factor the trinomial completely by using any method. remember to look for a common factor first. 3v² - 2v - 16

Write a function rule for  “the output is  5 less than the input.” let  xx  be the input and let  yy  be the output.

Sally deposited money into a savings account paying 4% simple interest per year. the first year, she earned $75 in interest. how much interest will she earn during the following year?