PSLE
Xuan baked some shortbreads. She gave ¹₂ of the shortbreads to her friends and 150 to her relatives. She was left with ¹₅ of the shortbreads. She packed these into 10 boxes. Some boxes contained 7 shortbreads while the rest contained 12 shortbreads.

1. How many shortbreads were packed into the 10 boxes?
2. How many boxes contained 12 shortbreads?

(a)
Fraction of the shortbreads given to her relatives
= 1 - ¹₂ - ¹₅

= 1 - ⁵₁₀ - ²₁₀
= ³₁₀

Number of shortbreads that Xuan gave to her relatives = 3 u

3 u = 150

1 u = 150 ÷ 3 = 50

Number of shortbreads that were packed in 10 boxes
= 2 u
= 2 x 50
= 100

Number of shortbreads that were packed in 10 boxes = 100

Boxes of 12	Shortbreads	Boxes of 7	Shortbreads	Total shortbreads
10	120	0	0	120
9	108	1	7	115

If all the shortbreads are packed in boxes of 12, the number of shortbreads needed
= 10 x 12
= 120

Small difference
= 120 - 115
= 5

Big difference
= 120 - 100
= 20

Number of boxes of 7 shortbreads 
= 20 ÷ 5
= 4

Number of boxes of 12 shortbreads
= 10 - 4
= 6

Answer(s): (a) 100; (b) 6