In a shop, the prices of pastries are listed as follow:
Pastry Prices |
Tart |
$1 |
Scone |
$3 |
Muffin |
$4 |
The ratio of the number of tarts sold to the number of scones sold was 6 : 5. The ratio of the number of muffins sold to the number of scones sold was 2 : 1. The shop collected $32 more on the sales of muffins than the sales of tarts.
- How many tarts were sold?
- How much did the shop collect from the sales of the pastries?
Tarts |
Scones |
Muffins |
6x2 |
5x2 |
|
|
2x5 |
1x5 |
12 u |
10 u |
5 u |
|
Tarts |
Scones |
Muffins |
Number |
12 u |
10 u |
5 u |
Value |
1 |
3 |
4 |
Total value |
12 u |
30 u |
20 u |
(a)
The number of scones sold is repeated. Make the number of scones the same. LCM of 5 and 2 is 10.
Amount that the shop collected more from the sales of the muffins than the tarts
= 20 u - 12 u
= 8 u
8 u = 32
1 u = 32 ÷ 8 = 4
Number of tarts that the cafe sold
= 12 u
= 12 x 4
= 48
(b)
Amount that the shop collected from the sales of the pastries
= 12 u + 30 u + 20 u
= 62 u
= 62 x 4
= $248
Answer(s): (a) 48; (b) $248