Translate each of the following sentences into a mathematical equation.

Transcription

1 Intermediate Algebra section 1.2 Linear equation word problems Ex1, Translate each of the following sentences into a mathematical equation. (a) 4 times the sum of a number and 3 is 40. (b) 4 less than 3 times a number is 41. (c) 4 times 3 less than a number is 40 (d) square of the sum of a number and 3 is 49 Ex2, Translate each of the following phrases or sentences into a mathematical expression or equation. (a) sum of two consecutive integers is 333. (b) sum of three consecutive integers is 333. (c) sum of three consecutive odd integers is 333. (d) length of a rectangle is 4 inches less than its width. (e) the square of the sum of a number and 2. Ex3, Width of a rectangle is 4 inches shorter than its length. Perimeter of the rectangle is 32 inches. Ex4, Length of a rectangle is 4 inches longer than twice its width. Perimeter of the rectangle is 68 inches. Ex5, A clothing store is having a sale. Esther paid $28 for a shirt which was discounted 20%. Find the price before the discount. (ignore tax) Ex6, At a restaurant, Aaron paid $92 for the entire food bill which included 15% tip. Find the amount of bill before the tip. Ex7*, A book regularly sells for $120. The sale price is $75. What is the discount rate?

2 A = C Proportion: B D Ex8, Annual property tax on a $800,000 property is $10,000. At the same tax rate, what is the property tax on a 1 million dollar property. 2 Ex9, Distance between 2 points A and B is 60 miles. On a certain map, the 2 points A and B are 3 inch apart. If the distance between points A and C are 4 inches on the same map, what is the real distance between points A and C? Ex10, of an ounce of sugar is needed to make a 7 quarts of certain kind of drink. At the same rate, how much sugar is needed to produce 9 quarts of that drink? Geometry problems (1) rectangle of sides a and b: P = 2(a+b), A= ab 1 (2) triangle of base b and height h, A = 2bh (3) box of dimensions a, b, c sa = 2(ab+bc+ac), V = abc Def Thm (1) Angles A and B are complementary angles if m( na) + m( nb) = 90 degrees. (2) Angles A and B are supplementary angles if m( na) + m( nb) = 180 degrees. Sum of 3 interior angles in a triangle equals 180 degrees. Ex11, Given a rectangle, its length is 3 inches more than its width. The perimeter of the rectangle is 28 inches. Find the length and the width of the rectangle. Ex12, Given a rectangle, the ratio of length to width is 4:3. ( width = 3 ) 2 The area of the rectangle is 300 in. Find the length and the width of the rectangle. length 4 Ex13, In a triangle, second angle is 20 degrees more than the first angle. The third angle is 35 degrees larger than the second angle. What are the angles in the triangle?

3 Intermediate Algebra section 1.2 Uniform rate problems Types of problems: RT = D (speed) (time duration) = (distance) RA = E (Rate)(amount of solution) = (amount of pure element) RP = I (interest rate)(principle) = (interest) RT = W (rate of work) (time duration) = (work) RT=D problems mixture problems interest problems work problems Ex14, A principle of $12,000 was invested into 2 accounts. One account was invested in muni bonds which generated 6% interest rate. The other account was invested in natural resources at 8% interest rate. The total interest amount from the 2 accounts was $920. Find the amount invested in each account. Ex15, How many gallons of 10% alcohol must be mixed with how many gallons of 4% alcohol to produce 24 gallons of 8% alcohol solution? Ex16, For the following problems, set up an equation (or a system of equations), then solve. We have 24 gallons of 10% lemonade. How much of (a) 16% lemonade must be added to produce 13% lemonade? (b) pure lemon juice must be added to produce 40% lemonade? (c) pure water must be added to produce 6% lemonade?

4 Ex17, Joshua has a total of 23 coins of quarters and nickels. Total value is $ How many of each kind of coins does he have? Ex18, Peter lives in Seattle and Paula lives in Vancouver. The 2 cities are 150 miles apart. At 10am, Peter leaves Seattle and drives towards Paula at 65 miles per hour, and at the time, Paula leaves Vancouver and drives towards Peter at 55 miles per hour. At what time do they meet? Ex19, Nina left her house in Los Angeles at 10am, driving at 55 miles per hour. Her brother Jonathan leaves the same house in Los Angeles at 11:30am and drives at 65 miles per hour towards Nina. At what time will Jonathan meet Nina.

5 Ex20, A boat travels at 7 miles/hour in still water. The boat makes a trip upstream against the current of a river in 20 minutes. The boat makes a return trip downstream with the current in 15 minutes. Find the speed of the current of the river? Ex21, Vesta can paint a house in 12 hours and Clorinda can paint the same house in 8 hours. If the 2 ladies paint the same house together, how long does it take? Ex22, Russell can pick 10 baskets of apples in 3 hours. If Russell and Juliady pick 10 baskets of apples together, it takes only 2 hours. If Juliady picks 10 baskets of apples by himself, how long does take it?