The Great Store held a promotion during the Christmas season.
- Jean spent $360 on each type of items. How many more mugs than plates did she buy?
- Rachel bought an equal number of plates and mugs. She paid $315 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 9 and 10 = 90
Number of sets of 5 plates that can be bought with $90
= 90 ÷ 10
= 9
Number of sets of 6 mugs that can be bought with $90
= 90 ÷ 9
= 10
Number of plates that can be bought with $90
= 9 x 5
= 45
Number of mugs that can be bought with $90
= 10 x 6
= 60
Difference in number of mugs and plates for every $90 spent on each item type
= 60 - 45
= 15
Number of sets of $90 in $360
= 360 ÷ 90
= 4
Number of more mugs than plates that Jean bought
= 4 x 15
= 60
(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 6 = 30
One set = 30 plates + 30 mugs
Cost of 30 plates
= 30 ÷ 5 x 10
= $60
Cost of 30 mugs
= 30 ÷ 6 x 9
= $45
Cost of one set of 30 plates and 30 mugs
= 60 + 45
= $105
Number of sets of 30 plates and 30 mugs
= 315 ÷ 105
= 3
Total number of mugs and plates in one set
= 2 x 30
= 60
Total number of mugs and plates that Rachel bought
= 3 x 60
= 180
Answer(s): (a) 60; (b) 180