In a pastry shop, the prices of pastries are listed as follow:
Pastry Prices |
Sandwich |
$1 |
Scone |
$3 |
Tart |
$5 |
The ratio of the number of sandwiches sold to the number of scones sold was 2 : 1. The ratio of the number of tarts sold to the number of scones sold was 3 : 2. The pastry shop collected $20 more on the sales of tarts than the sales of sandwiches.
- How many sandwiches were sold?
- How much did the pastry shop collect from the sales of the pastries?
Sandwiches |
Scones |
Tarts |
2x3 |
1x3 |
|
|
3x1 |
2x1 |
6 u |
3 u |
2 u |
|
Sandwiches |
Scones |
Tarts |
Number |
6 u |
3 u |
2 u |
Value |
1 |
3 |
5 |
Total value |
6 u |
9 u |
10 u |
(a)
The number of scones sold is repeated. Make the number of scones the same. LCM of 1 and 3 is 3.
Amount that the pastry shop collected more from the sales of the tarts than the sandwiches
= 10 u - 6 u
= 4 u
4 u = 20
1 u = 20 ÷ 4 = 5
Number of sandwiches that the cafe sold
= 6 u
= 6 x 5
= 30
(b)
Amount that the pastry shop collected from the sales of the pastries
= 6 u + 9 u + 10 u
= 25 u
= 25 x 5
= $125
Answer(s): (a) 30; (b) $125