MATH 110 Chapter 1 Review 05-11 - The Learning Lab at HFCC

MATH 110: CHAPTER 1 REVIEWCan you solve linear equations in one variable algebraically and check your answers by hand? (1.5)(1) (a) ( ) ( )10 a + 8 − 8 = 2 36 + 4a + 2a(b) 3 t + 2 8 − 2 t= − 43 4(c)m − 2 1−4m− = 23 53 4 ⎛ 3 ⎞+ ⎜ − 6 ⎟ = 2 + 1 + 62 3 ⎝ 8 ⎠(d) x x ( x )Can you solve linear equations in one variable by using a graphing calculator? (1.5)(2) (a) ( x ) x ( x )2 − 8 + = 3 − 6 + 2(b) 3 x − 2 5 − 2 x= − − 43 4(c)x − 3 4 − x− = 22 53 4 ⎛ 3 ⎞+ ⎜ + 6 ⎟ = 2 −1 − 62 3 ⎝ 8 ⎠(d) x x ( x )Revised 05/11 1

Can you set up and solve word problems involving linear equations? (1.6)(3) (a) Twice the difference of a number and 3 is the same as 1 added to three times the number.Find the number.(b) The new governor of California makes $27,500 more than the governor of New York, and$120,724 more than the governor of Alaska. If the sum of these 3 salaries is $471,276, findthe salary of each governor.(c) A premedical student at a local college was complaining that she had just paid $86.11 for heralgebra book, including tax. Find the price of the book before taxes if the tax rate at thiscollege is 9%.(d) Find the measures of the angles of a triangle whose two base angles are equal and whosethird angle is 12° less than twice the base angle.(e) The length of a rectangular playing field is 5 meter less than twice its width. If 230 meters offencing goes around the field, find the dimensions of the field.(f) The sum of the second and fourth of four consecutive integers is 186. Find the four integers.(g) A car rental company charges $19.95 per day for a compact car plus 12 cents per mile forevery mile over 100 miles driven per day. If Mr. Woo’s bill for 2 days’ use is $46.86, findhow many miles he drove.Revised 05/11 2

Can you create tables and use tables to solve problems? (1.7)(4) A local gas station has 1000 gallons of premium gasoline and has been selling it at a rate of 1.5gallons per minute.(a) Write an algebraic representation for the number of gallons, y1, in terms of the numbers ofminutes that have passed, x . (Assume no gasoline is delivered.)(b) Complete the table for the gallons of gasoline remaining given the number of minutes thathave elapsed.Minutes Elapsed 0 60 120 180 240 300 360Gallons Remaining(c) If the station does not get a gasoline delivery, when will the station run out of premium gas?(5) Judy Martinez has been shopping for school clothes and has picked out several outfits. Sheknows that the following Thursday there will be a Super Thursday sale and everything in thestore will be discounted 35%.(a) Write an algebraic representation for the sale price, y1, in terms of the price, x , on the pricetag. (Without tax.)(b) Complete the table and find the cost of each item on sale given the price on the price tag(Without tax.) Round to the nearest cent.Item Shirt Dress Shorts Shoes Purse Earrings BackpackPrice Tag $29.95 $35.95 $19.25 $39.95 $17.95 $9.95 $25.75Sale Price(c) If she purchases all the items when on sale, what will her total bill be before taxes?(d) What is the total after taxes if a 7% tax is added to the bill?(e) How much did she save before taxes by waiting for the sale?Revised 05/11 3

Answers:(1) (a) All real numbers16(b) t = −943(c) m =17(d) No solutions or ∅(2) (a) All real numbers. Both sides of the equations form the same line.y987654321x−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10−1−2−3−4−5−6−7−8−9−10(b) The lines intersect at x = − 9.16 or1x = − 9 6y4321x−14 −13 −12 −11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5−1(c) The lines intersect at x = 6.14286 or98765432y−2−3−4−5−6−7−8−9−10−11−12−13−14−15x =4371x−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10−1−2−3−4−5−6−7−8−9−10(d) The lines do not intersect. Thus there is no solution or ∅y987654321x−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10−1−2−3−4−5−6−7−8−9−10Revised 05/11 4

(3) (a) The number is -7(b) The California governor makes $206, 500, New York makes $179,000, and Alaska $85,776.(c) The book cost $79 before taxes.(d) The angles measure 48˚, 48˚, and 84˚.(e) The width is 40 m and the length is 75 m.(f) The integers are 91, 92, 93, and 94.(g) 258 miles(4) (a) y1 = 1000 − 1.5x(b)Minutes Elapsed 0 60 120 180 240 300 360Gallons Remaining 1000 910 820 730 640 550 4602(c) The station will run out of gas in 666 minutes; or 666 minutes 40 seconds, or 11 hours 63minutes 40 seconds.(5) (a) since the discount is 35%, the percentage of the price x that we WILL pay is100% - 35% = 65%. Thus the equation for the price should be y1 = 0.65x(b)Item Shirt Dress Shorts Shoes Purse Earrings BackpackPrice Tag $29.95 $35.95 $19.25 $39.95 $17.95 $9.95 $25.75Sale Price $19.47 $23.37 $12.51 $25.97 $11.67 $6.47 $16.74(c) $116.20(d) $124.33(e) $62.55Revised 05/11 5