PSLE
Yen baked a total of 42 large and small cakes in the ratio of 4 : 3. She decorated each cake with some lychees in the ratio of 7 : 2. She used a total of 312 lychees to decorate all the small cakes and 6 large cakes.

1. How many small cakes did Yen bake?
2. What was the number of lychees used to decorate all the small cakes?
3. How many more lychees did Yen 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	7 u	2 u
Total value	42 u	36 u	78 u

(b)
Number of lychees used to decorate 6 large cakes and 18 small cakes
= 42 u + 36 u
= 78 u

78 u = 312

1 u = 312 ÷ 78 = 4

Number of lychees used to decorate all the small cakes
= 36 u
= 36 x 4
= 144

(c)
Number of lychees to decorate one large cake
= 7 u
= 7 x 4
= 28

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

Number of more lychees that Yen needed to decorate the remaining large cakes
= 18 x 28
= 504

Answer(s): (a) 18; (b) 144; (c) 504