Solution to GrpC1:
John bought an equal number of pens and rulers for $9.80. A pen cost $1 and a ruler cost 40 cents. How much did he spend on the pens?
Since the number of pens and rulers is equal, we treat 1 pen and 1 ruler as a set:
1p + 1r à 100 + 40 = 140
980 ÷ 140 = 7 sets
That means he bought 7 pens and 7 rulers altogether.
7 ´ $1 = $7 Ans: $7
Solution to GrpC2:
Lucy had a total of $380, consisting of $2 and $5 notes. Given that she had 7 times as many $2 notes as $5 notes, how many notes did she have?
Since the number of $2 notes is 7 times the number of $5 notes, we treat 7 $2 notes and 1 $5 note as a set:
7e + 1f à (7 ´ 2) + 5 = 19 (Amount for 1 set)
380 ÷ 19 = 20 sets
That means Lucy had (7 ´ 20) $2 notes and 20 $5 notes altogether.
(7 ´ 20) + 20 = 160 Ans: 160
Solution to GrpC3:
Bala bought 2 more belts than wallets and paid a total of $154. Each belt cost $20 and each wallet cost $18. How many belts did he buy?
Since the number of belts is 2 more than the number of wallets, we remove 2 belts from the total. Then, we treat 1 belt and 1 wallet as a set:
2b à 2 ´ 20 = 40 (Cost of 2 belts being taken out)
154 – 40 = 114 (Cost of remaining belts and wallets)
1b + 1w à 20 + 18 = 38 (Cost of 1 set)
114 ÷ 38 = 3 sets
That means Bala bought (3 + 2) belts and 3 wallets altogether.
3 + 2 = 5 Ans: 5 belts
Solution to GrpC4:
A clock and a watch cost $120. Tom paid $840 for 5 clocks and 8 watches. How much does each watch cost?
Since the number of watches is 3 more than the number of clocks, we remove 2 watches from the total. Then, we treat 1 clock and 1 watch as a set:
1c + 1w à 120 (Cost of 1 set)
5c + 5w à 5 ´ 120 = 600 (Cost of 5 sets)
840 – 600 = 240 (Cost of remaining 3 watches)
240 ÷ 3 = 80 (Cost of 1 watch)
Ans: $80
Solution to GrpC5:
Wendy sold some apple tarts and vanilla tarts for $153. Each apple tart cost $2 and each vanilla tart cost 5⁄8 as much as the apple tart. 3⁄5 of the tarts sold were apple tarts. How many vanilla tarts did Wendy sell?
1 vanilla tart cost 5⁄8 as much as the apple tart, so:
1v à 5⁄8 ´ $2 = $1.25 (Cost of 1 vanilla tart)
Since 3⁄5 of the tarts sold were apple tarts, we treat 3 apple tarts and 2 vanilla tarts as a set:
3a + 2v à (3 ´ 2) + (2 ´ 1.25) = 8.50 (Cost of 1 set)
153 ÷ 8.50 = 18 sets
This means that Wendy sold (18 ´ 3) apple tarts and (18 ´ 2) vanilla tarts.
18 ´ 2 = 36 Ans: 36 vanilla tarts
Solution to GrpC6:
Ali spent $92 on an equal number of novels and magazines. Each novel cost $15 and each magazine cost $7 less than each novel. How much more did he spend on the novels than the magazines?
There were an equal number of novels and magazines, so we treat 1 novel and 1 magazine as a set. Also each magazine cost $6 less than each magazine, so:
1m à 15 – 7 = 8 (Cost of 1 magazine)
1n + 1m à 15 + 8 = 23 (Cost of 1 set)
92 ÷ 23 = 4 sets
This means he bought 4 novels and 4 magazines.
4 ´ 7 = 28 Ans: $28
