In a pastry shop, the prices of pastries are listed as follow:
Pastry Prices |
Sandwich |
$1 |
Tart |
$2 |
Muffin |
$4 |
The ratio of the number of sandwiches sold to the number of tarts sold was 6 : 5. The ratio of the number of muffins sold to the number of tarts sold was 4 : 3. The pastry shop collected $216 more on the sales of muffins than the sales of sandwiches.
- How many sandwiches were sold?
- How much did the pastry shop collect from the sales of the pastries?
Sandwiches |
Tarts |
Muffins |
6x4 |
5x4 |
|
|
4x5 |
3x5 |
24 u |
20 u |
15 u |
|
Sandwiches |
Tarts |
Muffins |
Number |
24 u |
20 u |
15 u |
Value |
1 |
2 |
4 |
Total value |
24 u |
40 u |
60 u |
(a)
The number of tarts sold is repeated. Make the number of tarts the same. LCM of 5 and 4 is 20.
Amount that the pastry shop collected more from the sales of the muffins than the sandwiches
= 60 u - 24 u
= 36 u
36 u = 216
1 u = 216 ÷ 36 = 6
Number of sandwiches that the cafe sold
= 24 u
= 24 x 6
= 144
(b)
Amount that the pastry shop collected from the sales of the pastries
= 24 u + 40 u + 60 u
= 124 u
= 124 x 6
= $744
Answer(s): (a) 144; (b) $744