PSLE
Barbara baked a total of 42 large and small cakes in the ratio of 4 : 3. She decorated each cake with some grapes in the ratio of 5 : 2. She used a total of 132 grapes to decorate all the small cakes and 6 large cakes.

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

(a)
Fraction of the cakes that were large ones = ⁴_{4 + 3} = ⁴₇

Number of large cakes
= ⁴₇ x 42
= 24

Number of small cakes
= 42 - 24
= 18

	Large cakes	Small cakes	Total
Number	6	18
Value	5 u	2 u
Total value	30 u	36 u	66 u

(b)
Number of grapes used to decorate 6 large cakes and 18 small cakes
= 30 u + 36 u
= 66 u

66 u = 132

1 u = 132 ÷ 66 = 2

Number of grapes used to decorate all the small cakes
= 36 u
= 36 x 2
= 72

(c)
Number of grapes to decorate one large cake
= 5 u
= 5 x 2
= 10

Number of remaining large cakes that were decorated yet
= 24 - 6
= 18

Number of more grapes that Barbara needed to decorate the remaining large cakes
= 18 x 10
= 180

Answer(s): (a) 18; (b) 72; (c) 180