In a pastry shop, the prices of pastries are listed as follow:
Pastry Prices |
Scone |
$1 |
Sandwich |
$3 |
Muffin |
$5 |
The ratio of the number of scones sold to the number of sandwiches sold was 3 : 2. The ratio of the number of muffins sold to the number of sandwiches sold was 7 : 4. The pastry shop collected $95 more on the sales of muffins than the sales of scones.
- How many scones were sold?
- How much did the pastry shop collect from the sales of the pastries?
Scones |
Sandwiches |
Muffins |
3x7 |
2x7 |
|
|
7x2 |
4x2 |
21 u |
14 u |
8 u |
|
Scones |
Sandwiches |
Muffins |
Number |
21 u |
14 u |
8 u |
Value |
1 |
3 |
5 |
Total value |
21 u |
42 u |
40 u |
(a)
The number of sandwiches sold is repeated. Make the number of sandwiches the same. LCM of 2 and 7 is 14.
Amount that the pastry shop collected more from the sales of the muffins than the scones
= 40 u - 21 u
= 19 u
19 u = 95
1 u = 95 ÷ 19 = 5
Number of scones that the cafe sold
= 21 u
= 21 x 5
= 105
(b)
Amount that the pastry shop collected from the sales of the pastries
= 21 u + 42 u + 40 u
= 103 u
= 103 x 5
= $515
Answer(s): (a) 105; (b) $515