Arithmatic english 4

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– ALGEBRA – and $5.50(x + 10) is the total amount spent. Write an equation that adds the ﬁrst two amounts and sets it equal to the total amount. 4.00(x) + 6.40(10) = 5.50(x + 10) Multiply through the equation: 4x + 64 = 5.5x + 55 Subtract 4x from both sides: 4x – 4x + 64 = 5.5x – 4x + 55 Subtract 55 from both sides: 64 – 55 = 1.5x + 55 – 55 9 1.5x Divide both sides by 1.5: 1.5 1.5 6=x You need 6 pounds of the $4.00 per pound coffee. The correct answer is b. Distance Problems Most problems that involve motion or traveling will probably use the formula distance = rate×time. Wendy drove 4 hours in a car to reach a conference she was attending. On her return trip, she followed 1 the same route but the trip took her 1 2 hours longer. If she drove 220 miles to conference, how much slower was her average speed on the return trip? a. 10 b. 15 c. 25 d. 40 e. 55 Use the formula distance = rate × time and convert it to distance = rate. Remember that the distance was time 1 1 220 miles for each part of the trip. Since it took her 4 hours to reach the conference, then 4 + 1 2 = 5 2 hours 220 for the return trip. = 40 miles per hour. However, the question did not ask for the speed on the way back; 5.5 it asked for the difference between the speed on the way there and the speed on the way home. The speed on 220 the way there would be = 55 miles per hour and 55 – 40 = 15 miles per hour slower on the return trip. 4 The correct answer is b. 353
– ALGEBRA – R atio Word Problems You can often use the ratio to help. Three-ﬁfths of the employees at Company A work overtime each week and the other employees do not. What is the ratio of employees who do not work overtime to the employees that do? a. 2 to 5 b. 3 to 5 c. 2 to 3 d. 3 to 2 e. 5 to 2 This is a case where the part is the employees who work overtime and the whole is the total number of Part 3 employees who work overtime this must imply that 2 employees who do not work overtime employees. Using Whole : 5 . Then . total employees 5 total employees 2 employees who do not work overtime Therefore, the ratio , which is equivalent to choice c. Be careful; you were not 3 employees who do not work overtime looking for the ratio of employees who do not work overtime to the total employees, which would have been choice a. Work Problems For this particular type of problem, think about how much of a job will be completed in one hour. Jason can mow a lawn in 2 hours. Ciera can mow the same lawn in 4 hours. If they work together, how many hours will it take them to mow the same lawn? a. 1 hour 20 minutes b. 1 hour 30 minutes c. 1 hour 45 minutes d. 2 hours 20 minutes e. 3 hours Think about how much of the lawn each person completes individually. Since Jason can ﬁnish in 2 1 hours, in 1 hour he completes 2 of the lawn. Since Ciera can ﬁnish in 4 hours, then in 1 hour she completes 1 1 of the lawn. If we let x = the time it takes both Jason and Ciera working together, then is the amount of 4 x the lawn they ﬁnish in 1 hour working together. Then use the equation 1 1 1 and solve for x. 2 4 x 1 1 1 2 4 x 354
– ALGEBRA – 1 1 1 Multiply each term by the LCD of 4x : 4x 1 2 4x 1 2 4x 1 2 2 4 x The equation becomes 2x + x = 4 Combine like terms: 3x = 4 3x 4 Divide each side by 3: 3 3 11 hours Therefore x 3 1 1 Since of an hour is of 60 minutes, which is 20 minutes, the correct answer is a. 3 3 F unctions Functions are a special type of equation often in the form f(x). Suppose you are given a function such as f(x) = 3x + 2. To evaluate f(4), substitute 4 into the function for x. f (x) = 3x + 2 f (4) = 3 (4) + 2 = 12 + 2 = 14 355
CHAPTER 22 Geometry This section reviews some of the terms that you should be familiar with for the Quantitative section. Be aware that the test will probably not ask you for a particular deﬁnition; instead, it will ask you to apply the concept to a speciﬁc situation. An understanding of the vocabulary involved will help you do this. Here are a few basic terms: A point is a location in a plane. ■ A line is an inﬁnite set of points contained in a straight path. ■ A line segment is part of a line; a segment can be measured. ■ A ray is an inﬁnite set of points that start at an endpoint and continue in a straight path in one direc- ■ tion only. A plane is a two-dimensional ﬂat surface. ■ 357
– GEOMETRY – A ngles Two rays with a common endpoint, called a vertex, form an angle. The following ﬁgures show the different types of angles: vertex Acute Right The measure is between 0 and 90 degrees. The measure is equal to 90 degrees. Obtuse Straight The measure is between 90 and 180 degrees. The measure is equal to 180 degrees. Here are a few tips to use when determining the measure of the angles. A pair of angles is complementary if the sum of the measures of the angles is 90 degrees. ■ A pair of angles is supplementary if the sum of the measures of the angles is 180 degrees. ■ If two angles have the same measure, then they are congruent. ■ If an angle is bisected, it is divided into two congruent angles. ■ Lines and Angles When two lines intersect, four angles are formed. 1 4 2 3 358