Download 2.3 2.4 application handout (INCLASS)

2.3 Applications of Linear Equations MAT1033 Pg 85 good chart for translations Ex from book 1, 2, 3 1. Translate each verbal expression as a mathematical expression. Use x for your variable. a) 9 added to a number b) The difference between 7 and a number c) Four times a number d) The quotient of 7 and a nonzero number 2. Translate each verbal sentence into an equation. Use x for your variable. a) The sum of a number and 6 is 28. b) If twice a number is decreased by 3, the result is 17. c) The product of a number and 7 is twice the number plus 12. d) The quotient of a number and 6, added to twice the number, is 7 3. Decide whether each is an expression or an equation. a) 5x – 3(x + 2) = 7 b) 5x – 3(x+2) 4. The length of a rectangle is 5cm more than its width. The perimeter is five times the width. What are the dimensions of the rectangle? 5. The Vietnam Veterans Memorial in Washington, DC is in the shape of two sides of an isosceles triangle. If the two walls of equal lengths were joined by a straight line of 438 ft, the perimeter of the resulting triangle would be 931.5 ft. Find the lengths of the two walls. 6. The John Hancock Center tapers as it rises. The top floor is rectangular and has a perimeter of 520 ft. The width of the top floor measures 20 ft more than one‐half its length. What are the dimensions of the top floor? 1 MAT 1033 2.3 Handout Linear Equation Applications 1) The length of a rectangular garden is 5 feet more than twice it width. If the perimeter of the garden is 52 feet, what are the dimensions of the garden? 2) the first side of a triangle is 5 cm less than the second side, and the third side is twice as long as the first side. If the perimeter of the triangle is 33 cm, find the length of the sides of the triangle. 3) Chris is selling apples and peaches. He has a total of 226 pieces of fruit altogether. If he has 50 more apples than he has peaches, how many pieces of each type of fruit does Chris have? 1) Ans: width – 7 ft., length – 19 ft 2) Ans: 7cm, 12 cm, & 14 cm 3) Ans: 88 Peaches, 138 apples 2 2.4 Further Applications of Linear Equations MAT1033 1. At the end of the day, a cashier had 26 coins consisting of dimes and half‐dollars. The total value of these coins was $8.60. How many of each type did he have? 2. Nana Nantamba found some coins while looking under her sofa pillows. There were equal numbers of nickels and quarters, and twice as many half‐dollars as quarters. If she found $2.60 in all, how many of each denomination of coins did she find? 3. Two cars leave the same location at the same time. One travels north at 60 mph and the other south at 45 mph. In how many hours will they be 420 mi apart? 4. Elayn begins jogging at 5:00 am averaging 3 mph. Clay leaves at 5:30 am following her, averaging 5 mph. How long will it take him to catch up to her? 5. One angle in a triangle is 15⁰ larger than a second angle. The third angle is 25⁰ larger than twice the second angle. Find the measure of each angle. 3 MAT 1033 Section 2.4 Distance Problems 1) Two planes start from the same point and fly in opposite directions. The first plane is flying 50 mph slower than the second plane. In 2 ½ hours the planes are 1400 miles apart. Find the rate of each plane. 2) A speeding car going 80 mph has a ½ hour head start on a helicopter trying to overtake the car. The helicopter is traveling at 130 mph. How far from the starting point does the helicopter overtake the car? 3) A cabin cruiser left a harbor and traveled to a small island at an average speed of 20 mph. On the return trip, the cabin cruiser traveled at an average speed of 12 mph because of fog. The total time for the trip was 5 hours. How far was the island from the harbor? 4) Jeff left home on his bicycle at 8:30 A.M. and averaged 5 miles per hour. His wife, Joan, left at 9:00 A.M., following the same path and averaging 8 miles per hour. At what time did Joan catch up with Jeff? 1) 250mph, 305 mph 2) 104 mi 3) 37.5 mi 4) 9:50 am 4