PSLE Penelope baked a total of 20 large and small cakes in the ratio of 7 : 3. She decorated each cake with some cranberries in the ratio of 3 : 2. She used a total of 216 cranberries to decorate all the small cakes and 4 large cakes.
- How many small cakes did Penelope bake?
- What was the number of cranberries used to decorate all the small cakes?
- How many more cranberries did Penelope need to decorate the remaining large cakes?
(a)
Fraction of the cakes that were large ones =
77 + 3 =
710Number of large cakes
=
710 x 20
= 14
Number of small cakes
= 20 - 14
= 6
|
Large cakes |
Small cakes |
Total |
Number |
4 |
6 |
|
Value |
3 u |
2 u |
|
Total value |
12 u |
12 u |
24 u |
(b)
Number of cranberries used to decorate 4 large cakes and 6 small cakes
= 12 u + 12 u
= 24 u
24 u = 216
1 u = 216 ÷ 24 = 9
Number of cranberries used to decorate all the small cakes
= 12 u
= 12 x 9
= 108
(c)
Number of cranberries to decorate one large cake
= 3 u
= 3 x 9
= 27
Number of remaining large cakes that were decorated yet
= 14 - 4
= 10
Number of more cranberries that Penelope needed to decorate the remaining large cakes
= 10 x 27
= 270
Answer(s): (a) 6; (b) 108; (c) 270