PSLE
Gillian baked some cupcakes. She gave ¹₂ of the cupcakes to her students and 78 to her colleagues. She was left with ¹₅ of the cupcakes. She packed these into 10 boxes. Some boxes contained 4 cupcakes while the rest contained 6 cupcakes.

1. How many cupcakes were packed into the 10 boxes?
2. How many boxes contained 6 cupcakes?

(a)
Fraction of the cupcakes given to her colleagues
= 1 - ¹₂ - ¹₅

= 1 - ⁵₁₀ - ²₁₀
= ³₁₀

Number of cupcakes that Gillian gave to her colleagues = 3 u

3 u = 78

1 u = 78 ÷ 3 = 26

Number of cupcakes that were packed in 10 boxes
= 2 u
= 2 x 26
= 52

Number of cupcakes that were packed in 10 boxes = 52

Boxes of 6	Cupcakes	Boxes of 4	Cupcakes	Total cupcakes
10	60	0	0	60
9	54	1	4	58

If all the cupcakes are packed in boxes of 6, the number of cupcakes needed
= 10 x 6
= 60

Small difference
= 60 - 58
= 2

Big difference
= 60 - 52
= 8

Number of boxes of 4 cupcakes 
= 8 ÷ 2
= 4

Number of boxes of 6 cupcakes
= 10 - 4
= 6

Answer(s): (a) 52; (b) 6