Word Problems with Equations
Q1. For each problem, define a variable and write an equation.
(a) A number increased by 8 gives 15. 1 mark
(b) Three times a number decreased by 4 equals 11. 1 mark
(c) The sum of two consecutive numbers is 35. 1 mark
(d) A rectangle's length is twice its width. The perimeter is 36 cm. 1 mark
Q2. Write an equation for each situation. Do not solve.
(a) A plumber charges $60 call-out fee plus $45 per hour. The total bill was $240. 1 mark
(b) A class has 28 students. There are 4 more girls than boys. 1 mark
(c) A mobile phone plan costs $30 per month plus $0.10 per text. The monthly bill was $42. 1 mark
Q3. A number is multiplied by 4, then 7 is subtracted. The result is 29. Find the number. 2 marks
Q4. The sum of three consecutive odd numbers is 63. Find the numbers. 2 marks
Q5. A rectangle has length 5 cm more than its width. The perimeter is 46 cm. Find the dimensions. 2 marks
Q6. Two angles in a triangle are equal. The third angle is 30° more than each of the equal angles. Find all three angles. 2 marks
Q7. A car rental company charges a flat fee of $80 plus $0.25 per kilometre. Another company charges $50 plus $0.40 per kilometre.
(a) Write an expression for the cost of hiring from each company for k kilometres. 1 mark
(b) Write an equation to find when both companies charge the same amount. 1 mark
(c) Solve the equation and interpret the result. 2 marks
(d) Which company is cheaper for a 150 km trip? Show your working. 1 mark
Answer Key
Q1. (a) n + 8 = 15 (b) 3n − 4 = 11 (c) n + (n + 1) = 35 (d) 2(2w + w) = 36 or 2l + 2(l/2) = 36
Q2. (a) 60 + 45h = 240 (b) b + (b + 4) = 28 (c) 30 + 0.10t = 42
Q3. 4n − 7 = 29, 4n = 36, n = 9
Q4. n + (n + 2) + (n + 4) = 63, 3n + 6 = 63, 3n = 57, n = 19. Numbers: 19, 21, 23.
Q5. l = w + 5; 2(w + 5 + w) = 46; 2(2w + 5) = 46; 4w + 10 = 46; 4w = 36; w = 9; l = 14. Dimensions: 9 cm × 14 cm.
Q6. x + x + (x + 30) = 180; 3x + 30 = 180; 3x = 150; x = 50. Angles: 50°, 50°, 80°.
Q7. (a) A = 80 + 0.25k, B = 50 + 0.40k (b) 80 + 0.25k = 50 + 0.40k (c) 30 = 0.15k, k = 200 km. Both charge the same at 200 km. (d) A: 80 + 0.25(150) = $117.50. B: 50 + 0.40(150) = $110. Company B is cheaper.
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