Practice with Algebraic Translations Topic Index | Algebra Index | Regents Exam Prep Center

Translate each of the following into an equation and solve if asked.

 1 Using the variable x to represent a number, write an algebraic equation for:        "twice a number increased by four equals 18". Answer 2x + 4 = 18

 2 Using the variable x to represent a number, write an inequality for: "three times a number decreased by four is at least fives time a number". Answer 3x - 4 >= 5x

 3 A formula about triangles defines a quantity s to be equal to one-half the sum of the three sides (a, b and c) of a triangle. Write this formula in mathematical notation. Solve the formula for a when s = 6,  b = 4 and c = 5. Answer Formula: s = 0.5(a + b + c) 6 = 0.5(a + 4 + 5) 6 = 0.5(a +9) 6 = 0.5a + 4.5 1.5 = 0.5a 3 = a

 4 A student receives \$10 a week for lunch in school.  The cafeteria charges \$1.60 for a plate lunch.  Write an equation to help the student calculate the amount of money, m, left after d days, assuming the student purchases the plate lunch each day. Answer m = 10 - 1.60d

 5 A recipe calls for 1/2 cup of chocolate chips.  Write a equation to determine the number of cups, c, of chocolate chips needed to make the recipe n times. Find the number of cups of chips needed to double the recipe. Answer c = 0.5 n Double means times 2. c = 0.5 (2) c = 1 cup of chips.

 6 The formula, f, for finding the number of stars in a quilt is the number of rows, r, times the number of columns, c.  Write a formula in mathematical notation for finding the number of stars. If there are 250 stars and there are 10 columns, how many rows of stars are in the quilt? Answer Formual: f = rc 250 = r(10) 25 = r 25 rows of stars

 7 A drive-in theater charges \$7 per vehicle plus \$1 for every person in the vehicle.  If the total charge is represented by T, and the number of people in the vehicle is represented by n, write an equation that can be used to find the cost per vehicle. What is the charge for a car with 6 people? Answer T = 7 + n Car with 6 people: T = 7 + 6 T = 13 The charge is \$13.

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