The Great Store held a promotion during the Christmas season.
- Xandra spent $80 on each type of items. How many more mugs than plates did she buy?
- Zara bought an equal number of plates and mugs. She paid $84 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 5 and 8 = 40
Number of sets of 4 plates that can be bought with $40
= 40 ÷ 8
= 5
Number of sets of 8 mugs that can be bought with $40
= 40 ÷ 5
= 8
Number of plates that can be bought with $40
= 5 x 4
= 20
Number of mugs that can be bought with $40
= 8 x 8
= 64
Difference in number of mugs and plates for every $40 spent on each item type
= 64 - 20
= 44
Number of sets of $40 in $80
= 80 ÷ 40
= 2
Number of more mugs than plates that Xandra bought
= 2 x 44
= 88
(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 4 and 8 = 8
One set = 8 plates + 8 mugs
Cost of 8 plates
= 8 ÷ 4 x 8
= $16
Cost of 8 mugs
= 8 ÷ 8 x 5
= $5
Cost of one set of 8 plates and 8 mugs
= 16 + 5
= $21
Number of sets of 8 plates and 8 mugs
= 84 ÷ 21
= 4
Total number of mugs and plates in one set
= 2 x 8
= 16
Total number of mugs and plates that Zara bought
= 4 x 16
= 64
Answer(s): (a) 88; (b) 64
