PSLE
Gwen baked a total of 35 large and small cakes in the ratio of 4 : 3. She decorated each cake with some cherries in the ratio of 3 : 2. She used a total of 312 cherries to decorate all the small cakes and 3 large cakes.

1. How many small cakes did Gwen bake?
2. What was the number of cherries used to decorate all the small cakes?
3. How many more cherries did Gwen 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 35
= 20

Number of small cakes
= 35 - 20
= 15

	Large cakes	Small cakes	Total
Number	3	15
Value	3 u	2 u
Total value	9 u	30 u	39 u

(b)
Number of cherries used to decorate 3 large cakes and 15 small cakes
= 9 u + 30 u
= 39 u

39 u = 312

1 u = 312 ÷ 39 = 8

Number of cherries used to decorate all the small cakes
= 30 u
= 30 x 8
= 240

(c)
Number of cherries to decorate one large cake
= 3 u
= 3 x 8
= 24

Number of remaining large cakes that were decorated yet
= 20 - 3
= 17

Number of more cherries that Gwen needed to decorate the remaining large cakes
= 17 x 24
= 408

Answer(s): (a) 15; (b) 240; (c) 408