Directions: Answer these questions pertaining to creating algebraic equations.

 1 Using the variable n to represent a number, write an algebraic equation for "twice a number increased by three equals twelve". Answer 2n + 3 = 12

 2 Using the variable x to represent a number, write an algebraic equation for "five less than the product of four and a number is ten". Answer 4x - 5 = 10

 3 Translate the following problem into an equation, letting c = cost and m = number of months: "The cost for high speed cable service is \$50 for the installation and \$35 a month for service." Answer c = 50 + 35m

 4 A formula regarding triangles defines a quantity s to be equal to one-half the sum of the sides of a triangle, where the sides are represented by a, b and c. Write this formula as an equation in mathematical notation. Answer c = ½(a + b + c)

 5 Translate the following problem into an equation, letting c = number of chips and w = number of walnuts: "A muffin recipe calls for twice as many chocolate chips as walnuts." Answer c = 2w

 6 Lights on the Lake charges \$10 per car plus \$2 for every person in the car. If the total charge is represented by T, and the number of people in the car is represented by n, a) write an equation that can be used to find the cost per car. b) find the charge for a car with 5 people. Answer a) T = 10 + 2n b) T = 10 + 2(5) = \$20

 7 Translate the following problem into an equation, letting t = total weight and g = number of gallons of water: "What is the total weight of an above ground pool, if the pool weighs 320 pounds and the water weighs 8.34 pounds per gallon?" Answer t = 8.34g + 320

 8 Jason receives \$15.00 per week for lunch in school. The cafeteria charges \$2.20 for a plate lunch. Write an equation that will determine the amount of money, m, the student will have left after d days. Assume that the student purchases only the plate lunch each day, and that d will be less than or equal to 5 days. Answer m = 15 - 2.20d

 9 Translate the following problem into an equation, letting O = number of oxygen atoms and H = number of hydrogen atoms: "H2O means that water contains two hydrogen atoms for every one oxygen atom." Answer H = 2O

 10 The formula for finding the number of flowers, f, in a rectangular garden is the number of rows, r, times the number of columns, c.  a) Write an equation in mathematical notation for finding the total number of flowers. b) If there are 300 total flowers in a rectangular garden and there are 15 columns in the garden, how many rows of flowers are in the garden? Answer a) f = r • c b) 20 rows

 11 If tennis rackets cost \$59 and racket covers cost \$15, how many of each can the tennis club purchase for \$237? Let r = racket and c = cover. Answer 59r + 15c = 237

 12 A cookie recipe calls for half a cup of M&M candies.   a) Write an equation to determine the number of cups, c, of M&Ms needed to make the recipe n times. b) Find the number of cups of M&Ms needed to double the recipe. Answer a) c = ½ • n b) 1 cup