PSLE
Penelope baked some biscuits. She gave ¹₁₀ of the biscuits to her relatives and 124 to her friends. She was left with ¹₂ of the biscuits. She packed these into 19 boxes. Some boxes contained 7 biscuits while the rest contained 9 biscuits.

1. How many biscuits were packed into the 19 boxes?
2. How many boxes contained 9 biscuits?

(a)
Fraction of the biscuits given to her friends
= 1 - ¹₁₀ - ¹₂

= 1 - ¹₁₀ - ⁵₁₀
= ⁴₁₀

Number of biscuits that Penelope gave to her friends = 4 u

4 u = 124

1 u = 124 ÷ 4 = 31

Number of biscuits that were packed in 19 boxes
= 5 u
= 5 x 31
= 155

Number of biscuits that were packed in 19 boxes = 155

Boxes of 9	Biscuits	Boxes of 7	Biscuits	Total biscuits
19	171	0	0	171
18	162	1	7	169

If all the biscuits are packed in boxes of 9, the number of biscuits needed
= 19 x 9
= 171

Small difference
= 171 - 169
= 2

Big difference
= 171 - 155
= 16

Number of boxes of 7 biscuits 
= 16 ÷ 2
= 8

Number of boxes of 9 biscuits
= 19 - 8
= 11

Answer(s): (a) 155; (b) 11