PSLE
Gillian baked a total of 49 large and small cakes in the ratio of 5 : 2. She decorated each cake with some grapes in the ratio of 3 : 2. She used a total of 430 grapes to decorate all the small cakes and 5 large cakes.

1. How many small cakes did Gillian bake?
2. What was the number of grapes used to decorate all the small cakes?
3. How many more grapes did Gillian need to decorate the remaining large cakes?

(a)
Fraction of the cakes that were large ones = ⁵_{5 + 2} = ⁵₇

Number of large cakes
= ⁵₇ x 49
= 35

Number of small cakes
= 49 - 35
= 14

	Large cakes	Small cakes	Total
Number	5	14
Value	3 u	2 u
Total value	15 u	28 u	43 u

(b)
Number of grapes used to decorate 5 large cakes and 14 small cakes
= 15 u + 28 u
= 43 u

43 u = 430

1 u = 430 ÷ 43 = 10

Number of grapes used to decorate all the small cakes
= 28 u
= 28 x 10
= 280

(c)
Number of grapes to decorate one large cake
= 3 u
= 3 x 10
= 30

Number of remaining large cakes that were decorated yet
= 35 - 5
= 30

Number of more grapes that Gillian needed to decorate the remaining large cakes
= 30 x 30
= 900

Answer(s): (a) 14; (b) 280; (c) 900