Arithmatic english 4 doc

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 Divide both sides by 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 the same route but the trip took her 1 ᎏ 1 2 ᎏ 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 = rate. Remember that the distance was 220 miles for each part of the trip. Since it took her 4 hours to reach the conference, then 4 + 1 ᎏ 1 2 ᎏ = 5 ᎏ 1 2 ᎏ hours for the return trip. = 40 miles per hour. However, the question did not ask for the speed on the way back; it asked for the difference between the speed on the way there and the speed on the way home. The speed on the way there would be = 55 miles per hour and 55 – 40 = 15 miles per hour slower on the return trip. The correct answer is b. 220 4 220 5.5 distance time 9 1.5 ϭ 1.5x 1.5 – ALGEBRA– 353 Ratio 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 employees. Using : . Then this must imply that . Therefore, the ratio , which is equivalent to choice c. Be careful; you were not 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 hours, in 1 hour he completes of the lawn. Since Ciera can finish in 4 hours, then in 1 hour she completes of the lawn. If we let x = the time it takes both Jason and Ciera working together, then is the amount of the lawn they finish in 1 hour working together. Then use the equation and solve for x. 1 2 ϭ 1 4 ϭ 1 x 1 2 ϭ 1 4 ϭ 1 x 1 x 1 4 1 2 2 3 ϭ employees who do not work overtime employees who do not work overtime 2 5 ϭ employees who do not work overtime total employees 3 5 ϭ employees who work overtime total employees Part Whole – ALGEBRA– 354 Multiply each term by the LCD of 4x : The equation becomes 2x + x = 4 Combine like terms: 3x = 4 Divide each side by 3: Therefore hours Since of an hour is of 60 minutes, which is 20 minutes, the correct answer is a.  Functions 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 1 3 1 3 x ϭ 1 1 3 3x 3 ϭ 4 3 4x 1 1 2 2ϩ 4x 1 1 4 2ϭ 4x 1 1 x 2 – ALGEBRA– 355 . 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 =. 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 1 3 1 3 x ϭ 1 1 3 3x 3 ϭ 4 3 4x 1 1 2 2ϩ 4x 1 1 4 2ϭ 4x 1 1 x 2 – ALGEBRA– 355