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# Algebra Review

### Regents Review

EquationSolution
Using the variable x to represent a number, write an algebraic equation for: "twice a number increased by four equals 18". 2x + 4 = 18
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". 3x - 4 >= 5x
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. s = 0.5(a + b + c)
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. m = 10 - 1.60d
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. c = 0.5n
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. f = rc
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. T = 7 + n
Solve for x: 3x + 5 = 11 x = 2
Solve for x: 2x + 1.8 = 4x - 4.4 x = 3.1
Solve for x: 8(x + 5) = 16 x = -3
Solve for x: 1/2 x + 6 = 10 x = 8
Solve for x: 5x - 4 - 2x + 1 = 8x + 2 x = -1
Ten times a number, increased by 8, is 58. Find the number. (Let x represent the number) x = 5
A number decreased by 20 equals 46. Find the number. (Let x represent the number) x = 66
A number divided by 5 equals 18. Find the number. (Let x represent the number) x = 90
If 7 is subtracted from a number, the result is 53. Find the number. (Let x represent the number) x = 60
If 9 is added to one-half of a number, the result is 29. Find the number. (Let x represent the number) x = 40
After he lost 14 pounds, Homer weighed 190 pounds. Find Homer's original weight. (Let x represent Homer's original weight in pounds) x = 204
A shop owner bought 8 dozen shirts. If he sold all but 18 of them, how many shirts did he sell? (Let x represent the number of shirts sold) x = 78
The cost of adding a garage to a home is 5 times as much as the cost of painting the house. If the garage addition costs \$15,000, find the cost of painting the house. (Let x represent the cost of painting the house in dollars) x = 3000
The length of a rectangle is 5 times the width. If the width is 7 meters, what is the length? (let x represent the length in meters) x = 35
After 2.5 feet had been cut from a piece of lumber, there were 9.5 feet left. What was the original length of the piece of lumber? (Let x represent the length of the original piece of lumber in feet) x = 12
Solve this system of equations using substitution: x + y = 1 x + 3y = 9 x = -3 y = 4
Solve this system of equations using substitution: 3x + y = 13 x + 6y = -7 x = 5 y = -2
Solve this system of equations using substitution: 5x - 2y = 3 2x - y = 0 x = 3 y = 6
Solve this system of equations using substitution: x + 2y = 8 x - 2y = 4 x = 6 y = 1
Created by: kimsteaching