PSLE
Gem baked some biscuits. She gave ¹₅ of the biscuits to her relatives and 135 to her friends. She was left with ⁷₂₀ of the biscuits. She packed these into 11 boxes. Some boxes contained 7 biscuits while the rest contained 11 biscuits.

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

(a)
Fraction of the biscuits given to her friends
= 1 - ¹₅ - ⁷₂₀

= 1 - ⁴₂₀ - ⁷₂₀
= ⁹₂₀

Number of biscuits that Gem gave to her friends = 9 u

9 u = 135

1 u = 135 ÷ 9 = 15

Number of biscuits that were packed in 11 boxes
= 7 u
= 7 x 15
= 105

Number of biscuits that were packed in 11 boxes = 105

Boxes of 11	Biscuits	Boxes of 7	Biscuits	Total biscuits
11	121	0	0	121
10	110	1	7	117

If all the biscuits are packed in boxes of 11, the number of biscuits needed
= 11 x 11
= 121

Small difference
= 121 - 117
= 4

Big difference
= 121 - 105
= 16

Number of boxes of 7 biscuits 
= 16 ÷ 4
= 4

Number of boxes of 11 biscuits
= 11 - 4
= 7

Answer(s): (a) 105; (b) 7