PSLE
Zara baked some cupcakes. She gave ¹₅ of the cupcakes to her students and 84 to her friends. She was left with ¹₂ of the cupcakes. She packed these into 15 boxes. Some boxes contained 6 cupcakes while the rest contained 11 cupcakes.

1. How many cupcakes were packed into the 15 boxes?
2. How many boxes contained 11 cupcakes?

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

= 1 - ²₁₀ - ⁵₁₀
= ³₁₀

Number of cupcakes that Zara gave to her friends = 3 u

3 u = 84

1 u = 84 ÷ 3 = 28

Number of cupcakes that were packed in 15 boxes
= 5 u
= 5 x 28
= 140

Number of cupcakes that were packed in 15 boxes = 140

Boxes of 11	Cupcakes	Boxes of 6	Cupcakes	Total cupcakes
15	165	0	0	165
14	154	1	6	160

If all the cupcakes are packed in boxes of 11, the number of cupcakes needed
= 15 x 11
= 165

Small difference
= 165 - 160
= 5

Big difference
= 165 - 140
= 25

Number of boxes of 6 cupcakes 
= 25 ÷ 5
= 5

Number of boxes of 11 cupcakes
= 15 - 5
= 10

Answer(s): (a) 140; (b) 10