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There were 173 motorcycles and cars in a car park. There were a total of 574 wheels.

There were 173 motorcycles and cars in a car park. There were a total of 574 wheels. How many motorcycles were there?. If all are cars, 4 × 173 = 692. If 1 is a motorcycle, 4 × 172 + 2 × 1 = 690. For every motorcycle in, every car out, 692 – 690 = 2. ? Motorcycles in, ? Cars out,

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There were 173 motorcycles and cars in a car park. There were a total of 574 wheels.

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  1. There were 173 motorcycles and cars in a car park. There were a total of 574 wheels. How many motorcycles were there? If all are cars, 4 × 173 = 692 If 1 is a motorcycle, 4 × 172 + 2 × 1 = 690 For every motorcycle in, every car out, 692 – 690 = 2 ? Motorcycles in, ? Cars out, 692 – 574 = 118 118 ÷ 2 = 59 (motorcycles) There were 59 motorcycles.

  2. A tennis ball cost $3 and a soccer ball cost $12. Ryan bought 60 tennis and soccer balls for $315. How many tennis balls and how many soccer balls did he buy? If all are soccer balls, 60 × 12 = 720 If 1 is a tennis ball, 59 × 12 + 1 × 3 = 711 For every tennis ball in, every soccer ball out, 720 – 711 = 9 ? Tennis balls in, ? Soccer balls out, 720 – 315 = 405 405 ÷ 9 = 45 (tennis balls) 60 – 45 = 15 There were 45 tennis balls and 15 soccer balls.

  3. 2 × 9 = 18 18 + 3 = 21 2 + 7 = 9 Peter had some pens. He gave Jeff half of the pens plus 3 pens. He gave Mark half of the remaining books plus 2 pens. If Peter had 7 pens left after this, how many pens did he have at first? 3 2 7 2 × 21 = 42 He had 42 pens at first.

  4. There were some marbles in a box. Bernard took of the marbles and another 7 marbles. Calvin took of the remaining marbles and another 6 marbles. If there were 36 marbles left, how many marbles were there in the box at first? 63 ÷ 3 = 21 36 + 6 = 42 42 + 14 + 7 = 63 36 42 ÷ 3 = 14 7 6 4 × 21 = 84 There were 84 marbles at first.

  5. Sam had thrice as many biscuits as sweets at first. After he gave away 16 sweets and 114 biscuits, he had four times as many sweets as biscuits left. Altogether, how many sweets and biscuits had he left? 114 1u B S 1u 1u 1u 1u 1u 1u 1u 1u 1u 1u 1u 1u 1u 1u 1u 1u 16 16 16 16 114 – 3 × 16 = 66 66 ÷ 11 = 6 (1 unit) 5 × 6 = 30 He had 30 biscuits left.

  6. Sally had half as many ribbons as hairclips at first. • After she gave away 15 ribbons and 150 hairclips, she had twice as many ribbons as hairclips left. • How many hairclips had she left? • How many ribbons had she at first? 1u 1u R C 1u 150 1u 1u 1u 1u 15 15 15 150 – 2 × 15 = 120 2 × 40 + 15 = 95 120 ÷ 3 = 40 (1 unit) (b) She had 95 ribbonsat first. (a) She had 40 hairclips left.

  7. There were some 20-cent coins in Drawer A and some 50-cent coins in Drawer B. The amount of money in Drawer B was $28.90 more than the amount of money in Drawer A. There were 46 more coins in Drawer A than in Drawer B. Find the amount of money in Drawer A. Value of coins No. of coins 20¢ 46 20¢ 50¢ $28.90 50¢ $9.20 + $28.90 = $38.10 46 × 20¢ = $9.20 $9.20 $9.20 Difference between 1 of each piece  50¢ – 20¢ = 30¢ Difference between ? pieces  $38.10 ÷ $0.30 = 127 (127 + 46) × 20¢ = $34.60 The amount of money in Drawer A was $34.60.

  8. A post office sold some 30¢ and $1 stamps. The value of the $1 stamps sold was $46.50 more than the value of the 30¢ stamps sold. There were 27 more 30¢ stamps sold than $1 stamps sold. Find the total amount of money collected from all the stamps sold. Value of coins No. of coins 30¢ 27 30¢ $1 $46.50 $1 $8.10 + $46.50 = $54.60 27 × 30¢ = $8.10 $8.10 $8.10 Difference between 1 of each piece  $1 – $0.30 = $0.70 Difference between ? pieces  $54.60 ÷ $0.70 = 78 (78 + 20) × $0.30 + 78 × $1 = $107.40 The amount of money collected was $107.40.

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