This is the marking copy and it carries every answer. Her sheet is the other file — same numbering, same margin codes, so you can mark straight down the page.
Andy bought 4 identical shirts at $12.80 each and spent the rest of the money on 8 identical pairs of socks. He gave $100 to the cashier and received 80 cents change. How much did each pair of socks cost?
answer 6
method He spent $100 − $0.80 = $99.20 in total. The shirts cost 4 × $12.80 = $51.20, so the socks cost $99.20 − $51.20 = $48. There are 8 pairs, so each pair is $48 ÷ 8 = $6.
watch Treating 80 cents as $80, or forgetting to take the change off the $100 before splitting the rest.
Mrs Thompson baked 175 tarts. She sold 3/5 of them. Each tart was sold for $4. How much money did she collect in total?
answer 420
method Find how many she sold: 1/5 of 175 is 35, so 3/5 is 3 × 35 = 105 tarts. Each sold for $4, so she collected 105 × $4 = $420.
watch Multiplying all 175 tarts by $4. She only sold three fifths of them — the unsold ones brought in nothing.
Shirley packed 163 lollipops into plastic bags of 7 lollipops. She used the most number of plastic bags possible. She sold each plastic bag of lollipops at $6 and each remaining lollipop at $2. How much did she get after selling all the lollipops?
answer 142
method Divide to find the bags: 163 ÷ 7 = 23 bags with 2 lollipops left over. The bags bring in 23 × $6 = $138, and the 2 loose lollipops bring in 2 × $2 = $4. Total = $138 + $4 = $142.
watch Throwing away the remainder. The 2 left-over lollipops are still sold — at a different price, which is exactly why the remainder matters here.
A glue stick cost $1.80. A pair of scissors cost $3.20. Thomas bought an equal number of glue sticks and scissors. He spent $25 in all. How many glue sticks and scissors did he buy in total?
answer 10
method Buy them in pairs, since the numbers are equal: one glue stick and one pair of scissors cost $1.80 + $3.20 = $5. Then $25 ÷ $5 = 5 pairs. Each pair is 2 items, so in total he bought 5 × 2 = 10 items.
watch Answering 5 — that is the number of PAIRS. The question asks for glue sticks and scissors added together.
A man changed $210 into $5 and $2 notes. The number of $5 notes and $2 notes was the same. How many $5 notes did he get?
answer 30
method Because the numbers are equal, take one of each together: $5 + $2 = $7 per pair. Then $210 ÷ $7 = 30 pairs, so he got 30 five-dollar notes (and 30 two-dollar notes).
watch Dividing $210 by $5 alone. The pairing is what makes the two equal counts usable in one division.
Mrs Sim wanted to buy 20 glass bowls but she was short of $8. She then bought 19 glass bowls and had $6 left. Each glass bowl cost the same. How much money did Mrs Sim have at first?
answer 272
method Compare the two plans. Buying one bowl fewer took her from being $8 short to having $6 spare — a swing of 8 + 6 = $14. That swing is the price of exactly one bowl, so a bowl costs $14. She bought 19 of them and had $6 left, so she started with 19 × $14 + $6 = $266 + $6 = $272.
watch Subtracting the 8 and the 6 instead of adding them. Being short and having spare are on opposite sides of zero, so the gap between the two plans is their sum.
The table shows the cost of pizza: a Regular is $12 and a Large is $22. Mrs Tan ordered 6 large pizzas and 5 regular pizzas. She gave the delivery man $200. How much change did Mrs Tan receive?
answer 8
method 6 large: 6 × $22 = $132. 5 regular: 5 × $12 = $60. Total = $132 + $60 = $192. Change from $200 = 200 − 192 = $8.
watch Answering 192 — that is what she spent, not the change. Or pairing the wrong price to the wrong size.
Star Bookshop is having a promotion: notebooks are $5 each, and for every 2 notebooks bought the third notebook is free (buy 3 for the price of 2). Karen bought 25 notebooks. What is the least amount of money she has spent in total?
answer 85
method Group the notebooks in threes, because every group of 3 costs only 2 × $5 = $10. In 25 notebooks there are 25 ÷ 3 = 8 groups of three (24 notebooks) with 1 left over. The 8 groups cost 8 × $10 = $80, and the last notebook has no partners so it costs the full $5. Total = $80 + $5 = $85.
watch Paying full price for all 25 ($125), or counting the free ones as groups of 2. The deal gives 3 notebooks for the price of 2, so it is groups of THREE that matter.
Ken had some money. He used 1/2 of it to buy a shirt and 1/5 of it to buy a pair of pants. He had $180 left. How much money did he have at first?
answer 600
method He spent 1/2 + 1/5 of his money. Using tenths: 5/10 + 2/10 = 7/10. So what is left is 10/10 − 7/10 = 3/10, and that is $180. One tenth is 180 ÷ 3 = $60, so the whole is 10 × $60 = $600.
watch Adding 1/2 and 1/5 as 2/7 by adding tops and bottoms. Fractions need a common denominator before they can be added.
Max bought the same number of books and files. Each book cost $7 and each file cost $2. He paid $243 altogether. How many books and files did he buy altogether?
answer 54
method Because the numbers are equal, buy them in pairs: one book and one file cost $7 + $2 = $9. Then $243 ÷ $9 = 27 pairs. Each pair is 2 items, so altogether he bought 27 × 2 = 54 books and files.
watch Answering 27 — that is the number of BOOKS (and of files), but the question asks for both kinds added together.
Mother bought 5 more cups than plates. Each cup cost $8 and each plate cost $3. She paid $183 altogether. How many cups did she buy?
answer 18
method Set the 5 extra cups aside first: they cost 5 × $8 = $40. That leaves $183 − $40 = $143 for equal numbers of cups and plates. One cup and one plate together cost $8 + $3 = $11, so there are $143 ÷ $11 = 13 pairs. So there are 13 plates and 13 + 5 = 18 cups.
watch Answering 13 — that is the number of PLATES (and of the matched cups). The five extra cups still have to be added on.
The total cost of 6 skirts and 3 blouses was $144. Three blouses cost as much as 2 skirts. Find the total cost of one skirt and one blouse.
answer 30
method Swap the blouses for skirts: 3 blouses cost the same as 2 skirts, so 6 skirts + 3 blouses costs the same as 6 skirts + 2 skirts = 8 skirts. So 8 skirts = $144, and one skirt = $18. Then 3 blouses = 2 skirts = $36, so one blouse = $12. One skirt and one blouse = $18 + $12 = $30.
watch Assuming a blouse costs the same as a skirt, or dividing $144 by 9 items. The swap is what makes everything one kind of thing.
Jason has $20. He bought 2 packets of chips and 6 oranges. Chips are $2.50 a packet and oranges are 3 for $1.20. How much money did he have left?
1 packet of chips $2.50 3 oranges for $1.20
(A) $7.40 (B) $7.80 (C) $10.30 (D) $12.60
answer (D) — $12.60
method Chips: 2 × $2.50 = $5.00. Oranges: 6 is two lots of 3, so 2 × $1.20 = $2.40. He spent $5.00 + $2.40 = $7.40. Money left = $20 − $7.40 = $12.60.
watch Answering $7.40 — that is what he SPENT. The question asks what is left, so there is one more subtraction to do.
A stall had a promotion: buy 1 muffin for $3 each, or buy 4 muffins at $11. Mandy wanted to buy 50 muffins. What was the least amount of money Mandy had to pay for all the 50 muffins?
Buy 1 muffin for $3 each Buy 4 muffins at $11
answer 138
method The 4-for-$11 deal works out at $2.75 a muffin, cheaper than $3, so take as many fours as possible: 50 ÷ 4 = 12 sets of four (48 muffins) with 2 left over. That is 12 × $11 = $132, plus 2 singles at $3 = $6. Total = $138. (Buying 13 sets would give 52 muffins for $143 — more muffins AND more money, so it is not cheaper.)
watch Buying 13 sets of four to avoid paying full price for the last two. Always price the leftover BOTH ways — here the singles win.
At a fruit stall, mangoes are sold at 2 for $7 and pears are sold at 3 for $5.50. Mdm Fauziah bought the same number of mangoes and pears. She paid $160 in total. How many mangoes did she buy?
Mangoes 2 for $7 Pears 3 for $5.50
answer 30
method Choose a number of each that both deals divide into — 6 is the smallest. 6 mangoes are three lots of 2, costing 3 × $7 = $21. 6 pears are two lots of 3, costing 2 × $5.50 = $11. So 6 of each costs $21 + $11 = $32. Then $160 ÷ $32 = 5 such groups, and she bought 5 × 6 = 30 mangoes.
watch Working out the price of one mango and one pear. A pear costs $5.50 ÷ 3, which is not a whole number of cents — buying in sixes keeps every figure exact.
A rectangular park measures 54 m by 28 m. A pedestrian path 2 m wide and a cyclist path 3 m wide are built along two sides of the park — the pedestrian path wraps the top and left of the park, and the cyclist path wraps the top and left of that. It costs $18 to construct each square metre of the cyclist path. How much does it cost to construct the cyclist path?
################################ -+ 3 m cyclist
##+--------------------------+## -+ 2 m pedestrian
##| | #
##| Park | # 28 m
##| | #
##+--------------------------+-+
|<-------- 54 m -------->|
# = the two paths, along the TOP and the LEFT onlyanswer 4806
method Build outwards from the park. The park is 54 by 28. Adding the 2 m pedestrian path along the top and the left makes that block 54 + 2 = 56 by 28 + 2 = 30. Adding the 3 m cyclist path along the top and left of THAT makes the whole thing 56 + 3 = 59 by 30 + 3 = 33. The cyclist path is the difference between those two: 59 × 33 − 56 × 30 = 1947 − 1680 = 267 m². At $18 a square metre, the cost is 267 × $18 = $4806.
watch Measuring the cyclist path's strips from the PARK's 54 and 28 instead of from the outside of the pedestrian path. The paths are stacked, so the outer one is longer than the inner one.