The Great Store held a promotion during the Christmas season.
- Rachel spent $54 on each type of items. How many more mugs than plates did she buy?
- Emma bought an equal number of plates and mugs. She paid $204 in all. How many mugs and plates did she buy altogether?
(a)
Since the amount spent on each item type is the same, we need to make the amount spent on each item type the same.
LCM of 6 and 9 = 18
Number of sets of 5 plates that can be bought with $18
= 18 ÷ 9
= 2
Number of sets of 8 mugs that can be bought with $18
= 18 ÷ 6
= 3
Number of plates that can be bought with $18
= 2 x 5
= 10
Number of mugs that can be bought with $18
= 3 x 8
= 24
Difference in number of mugs and plates for every $18 spent on each item type
= 24 - 10
= 14
Number of sets of $18 in $54
= 54 ÷ 18
= 3
Number of more mugs than plates that Rachel bought
= 3 x 14
= 42
(b)
Since the number of each item type is the same, we need to make the number of each item type bought the same.
LCM of 5 and 8 = 40
One set = 40 plates + 40 mugs
Cost of 40 plates
= 40 ÷ 5 x 9
= $72
Cost of 40 mugs
= 40 ÷ 8 x 6
= $30
Cost of one set of 40 plates and 40 mugs
= 72 + 30
= $102
Number of sets of 40 plates and 40 mugs
= 204 ÷ 102
= 2
Total number of mugs and plates in one set
= 2 x 40
= 80
Total number of mugs and plates that Emma bought
= 2 x 80
= 160
Answer(s): (a) 42; (b) 160