Write an expression in x that represents the length:

Transcription

1 Name Common Core Algebra I (H) Date Algebraic Word Problems Each problem has 2 or 3 unknown numbers. Label one of the unknowns as x, then label the other(s) in terms of x, write an equation, solve the equation, and finally answer the question. 1. Sally is Bob s younger sister, and she is 7 years younger than Bob. If you multiply Bob s age by three and subtract Sally s age, you get their mother s age, which is 37 years. How old is Sally? Let x be Bob s age. What expression in x represents Sally s age? Write an equation in x for this problem: Solve that equation (show all work): How old is Sally? 2. You have 540 feet of fencing to enclose a rectangular garden. You want the length of the garden to be 50 feet greater than the width. Find the length and width of the garden if you use all of the fencing. Let x be the width of the fence. Write an expression in x that represents the length: Write an equation in x that expresses the condition that the total amount of fencing is 540 feet: Solve that equation. What are the length and width of the garden? Page 1 of 5

2 3. A wire that is 76 inches long is bent to form a rectangle. If the length of this rectangle is 7 inches less than twice its width, then what is the area of the rectangle? Let x be the width of the rectangle. What expression (in x) represents the length? width 7 less than twice width Write an equation in x that expresses the condition that the wire is 76 inches long: Solve that equation for x. What is the area of the rectangle? 4. A triangle has perimeter of 92 cm. The longest side is twice as long as the shortest side, and the third side is 12 cm longer than the shortest side. How long is each side? Let x be the length of the shortest side. a. Label the lengths of the sides in terms of x: Shortest side = x Longest side = Other side = x b. Write an equation in x that represents, the perimeter is 92. c. Solve that equation. Page 2 of 5

3 5. Barry bought a book, a magazine and a pen for a total of $14.75 before tax. The book was 4 times as expensive as the magazine, and the pen was $5.50 less than the book. What was the price of the book? a. Label the unknowns: Price of Book = Price of Magazine = Price of Pen = 6. The sum of the angles in any triangle is 180 o. In triangle ABC, angle B is 5 o less than twice angle A, and angle C is 10 o less than angle B. What is the measure of angle B? a. Label the unknowns: Measure of angle A = Measure of angle B = Measure of angle C = Page 3 of 5

4 7. Bob is twice as old as Chuck, and Susie is 10 years younger than Bob. If the sum of their ages is 100 years, how old is Susie? a. Label the unknowns: Bob s age = Chuck s age = Susie s age = 8. Towns A, B, C, and D are on the same highway as shown: A B C D The distance from A to B is three times the distance from C to D, and the distance from B to C is 10 miles less than the distance from A to B. If the distance from A to D is 95 miles, how far is it from town B to town C? a. Label the unknowns: Distance from A to B = Distance from B to C = Distance from C to D = Page 4 of 5

5 9. A triangle has perimeter of 115 cm. The longest side is twice as long as the shortest side, and the third side is 10 cm shorter than the longest side. How long is each side? a. Label the unknowns: Shortest side = Longest side = Other side = 10. Mary has nothing but nickels, dimes and quarters in her purse. There are twice as many nickels as quarters, and three more dimes than nickels. If she has 58 coins in her purse, then how much money (dollar amount) does she have in the purse? a. Label the unknowns: Number of nickels = Number of dimes = Number of quarters = Page 5 of 5