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UNIVERSITY OF GUYANA, BERBICE CAMPUS DIVISION OF NATURAL SCIENCES DEPARTMENT OF COMPUTER SCIENCE, MATHEMATICS & STATISTICS MTH111 TUTORIAL W0RKSHEET # 3 Simple Equations Page 1 of 6 Page 2 of 6 Word Problems Leading to Simple Equations 1) A rectangle is three times as long as it is wide, and its perimeter is 56m. Find its dimensions. 2) Find three consecutive even numbers whose sum is 84. 3) A man walked for 2 hours at 3.75 km/h and then cycled for a time at 10 km/h. If he covered a distance of 22.5 km in total, for how long did he cycle? 4) A motorist travels regularly between two towns. He usually takes 5.75 hours by travelling at a certain speed, but he finds that if he increases his speed by 3km/h he can reduce the time by half an hour. Find his usual speed. 5) The three angles in a triangle are ( x – 25 )º, ( 2x + 40 )º and 30º, find the magnitude of each angle of this triangle. 6) Find three consecutive odd numbers whose sum is 57. 7) Find the number which when added to both the numerator and denominator of the fraction 2/3 gives the new fraction 6/7. 8) Kelly had 12 dollars and spent x dollars. Amy had 6 dollars and collected x dollars. The two girls then had the same amount of money. Form an equation and solve it to find the value of x. 9) A student bought 9 books. Some cost $6 each and the remainder cost $6.50 each. If the total amount spent was $56, how many of each was bought. 10) A trader buys n oranges at the rate of 5 for $4. 8 of the oranges are bad so she sells the rest at the rate of 4 for $4 and makes a profit of $18. How many oranges did she buy? 11) A man cycles to a village at 18 km/h and returns at 12 km/h. If he takes 6.25 hours for the double journey, how far does he ride altogether? 12) A total of m matches are needed to fill 30 matchboxes with the same number of matches in each box. a) How many matches are in each box? b) If 3 fewer matches are put in each box, there are enough for 32boxes. What is the value of m? 13) A water tank contains 5 times as much as another water tank. When 20 litres of water are poured from the first tank into the second, the first contains 3 times as much as the second. How much water did each tank contain originally? Page 3 of 6 Inequations SIMULTANEOUS LINEAR EQUATIONS 1) Solve by substitution: a) b) c) d) e) f) a) b) c) d) e) f) 2) Solve by Elimination: Page 4 of 6 3) Solve: a) d) b) c) – e) f) 4) Solve the equation: 5) A number of two digits is such that the sum of the digits is 11, and the number is 27 greater than the number obtained by reversing the digits. Find the number. 6) A racing eight can row three miles upstream in twenty minutes, and three miles downstream in 12 minutes. Find the speed of the current, and of the eight in still water. 7) A man running for 8 miles and walking for 2 miles covers 10 miles in 1 hr. 18min. If he runs 6 miles and walks 4 miles, the distance takes him 1 hr.36min.What are his running and walking speeds? 8) A man bicycles 52 miles in 5 hours, travelling at 8 m.p.h. for hours .Find and hours and at 12 m.p.h. for 9) Divide 75 into two parts so that one part is 2/3 of the other. 10) If 1 is added to both numerator and denominator of a fraction the fraction becomes ½ , if 8 is added to both, the fraction becomes 2/3. What is the fraction? Page 5 of 6 11) A bird laid a certain number of eggs in a nest, and a collector took away two –thirds of them. The bird laid some more, and another collector took two-thirds of them. If the bird laid 12 eggs altogether and collectors took 10 altogether how many eggs were there to begin with? 12) A school boy agrees with his schoolmaster that he will pay a penny for every sum he gets wrong if he wins 3 pence for every one he gets right. After doing 20 sums he is four dimes down. How many did he get right? 13) If hot and cold taps are turned on together a bath is filled in three minutes; but if the cold tap was only half opened it would take one minute forty eight seconds longer. How long would the hot tap alone take to fill the bath? 14) The sum of two numbers is 19 and their difference is 5 find the numbers. 15) A gardener makes a rectangular flower-bed square by taking two feet off its length and adding three feet to its breadth. By doing so he increases the area by 20 square feet. What is its final area? Page 6 of 6