In a pastry shop, the prices of pastries are listed as follow:
Pastry Prices |
Tart |
$1 |
Puff |
$3 |
Sandwich |
$4 |
The ratio of the number of tarts sold to the number of puffs sold was 6 : 5. The ratio of the number of sandwiches sold to the number of puffs sold was 5 : 4. The pastry shop collected $70 more on the sales of sandwiches than the sales of tarts.
- How many tarts were sold?
- How much did the pastry shop collect from the sales of the pastries?
Tarts |
Puffs |
Sandwiches |
6x1 |
5x1 |
|
|
5x1 |
4x1 |
6 u |
5 u |
4 u |
|
Tarts |
Puffs |
Sandwiches |
Number |
6 u |
5 u |
4 u |
Value |
1 |
3 |
4 |
Total value |
6 u |
15 u |
16 u |
(a)
The number of puffs sold is repeated. Make the number of puffs the same. LCM of 5 and 5 is 5.
Amount that the pastry shop collected more from the sales of the sandwiches than the tarts
= 16 u - 6 u
= 10 u
10 u = 70
1 u = 70 ÷ 10 = 7
Number of tarts that the cafe sold
= 6 u
= 6 x 7
= 42
(b)
Amount that the pastry shop collected from the sales of the pastries
= 6 u + 15 u + 16 u
= 37 u
= 37 x 7
= $259
Answer(s): (a) 42; (b) $259