Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Three consecutive integers add to −42. What is the largest of them?
Show worked solution
x + (x + 1) + (x + 2) = −42, so 3x + 3 = −42, 3x = −45 and x = −15. The integers are −15, −14, −13, so the largest is −13. −15 is the smallest; −14 is the middle one; −11 moves the 3 across without changing its sign (3x = −39).
2 Ana is 5 years older than Ben. In 3 years’ time their ages will add to 41. How old are they now?
Show worked solution
(b + 3) + (b + 5 + 3) = 41, so 2b + 11 = 41 and b = 15. Ben is 15 and Ana is 20. Check: in 3 years, 18 + 23 = 41.
3 The perimeter of this triangle is 45 cm. How long, in cm, is its longest side?
Show worked solution
(x + 4) + (2x − 1) + 3x = 45, so 6x + 3 = 45 and x = 7. The sides are 11, 13 and 21 cm, so the longest is 21 cm. Check: 11 + 13 + 21 = 45.
Level 2 · Core
4 A concert sold 120 tickets: adults at $15 and students at $9. Ticket sales came to $1494. How many student tickets were sold?
Show worked solution
9s + 15(120 − s) = 1494, so 1800 − 6s = 1494, 6s = 306 and s = 51. Check: 51 × 9 + 69 × 15 = 459 + 1035 = 1494. 69 is the number of adult tickets; 62.25 divides the total by $24 as if everyone paid both prices; 306 stops at 6s = 306.
5 A train runs for 4 hours, part of the time at 80 km/h and the rest at 110 km/h. It covers 380 km. How many hours does it spend at 80 km/h, and how many km does it cover at 110 km/h?
Show worked solution
80t + 110(4 − t) = 380, so 440 − 30t = 380 and t = 2 h. At 110 km/h for 2 h it covers 220 km. Check: 160 + 220 = 380.
6 A rectangle is 6 cm longer than a square and 2 cm narrower. The rectangle’s area is 20 cm2 more than the square’s. Find the side of the square, in cm.
Show worked solution
(x + 6)(x − 2) = x2 + 20, so x2 + 4x − 12 = x2 + 20. The x2 terms cancel: 4x = 32 and x = 8. Check: 14 × 6 = 84 and 64 + 20 = 84.
Level 3 · Challenge
7 Pens cost $3 and folders cost $5. Kai buys 4 more pens than folders and spends $60.
1 If f is the number of folders, 3(f + 4) + 5f = 60.
2 Kai buys 6 folders.
3 Kai buys 12 items altogether.
Which statements are correct?
1 If f is the number of folders, 3(f + 4) + 5f = 60.
2 Kai buys 6 folders.
3 Kai buys 12 items altogether.
Which statements are correct?
Show worked solution
Pens cost 3(f + 4) and folders 5f, so 3(f + 4) + 5f = 60 (1 ✓). 8f + 12 = 60 gives f = 6 (2 ✓). That is 6 folders and 10 pens: 16 items, not 12 (3 ✗). 1 and 2.
8 Four years ago a woman was 5 times as old as her son. In 6 years’ time she will be 3 times as old as him. How old are they now?
Show worked solution
Woman now = 5(s − 4) + 4 = 5s − 16. In 6 years: 5s − 10 = 3(s + 6), so 2s = 28 and s = 14. Son 14, woman 54. Check: 4 years ago 10 and 50; in 6 years 20 and 60.
9 Two cars leave the same town at the same time and drive in opposite directions. One is 15 km/h faster than the other. After 3 hours they are 345 km apart. What is the speed of the faster car, in km/h?
Show worked solution
3x + 3(x + 15) = 345, so 6x + 45 = 345, 6x = 300 and x = 50. The faster car travels at 65 km/h. Check: 150 + 195 = 345.