PSLE
Xuan baked some shortbreads. She gave ¹₂ of the shortbreads to her students and 45 to her friends. She was left with ⁷₂₀ of the shortbreads. She packed these into 17 boxes. Some boxes contained 5 shortbreads while the rest contained 7 shortbreads.

1. How many shortbreads were packed into the 17 boxes?
2. How many boxes contained 7 shortbreads?

(a)
Fraction of the shortbreads given to her friends
= 1 - ¹₂ - ⁷₂₀

= 1 - ¹⁰₂₀ - ⁷₂₀
= ³₂₀

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

3 u = 45

1 u = 45 ÷ 3 = 15

Number of shortbreads that were packed in 17 boxes
= 7 u
= 7 x 15
= 105

Number of shortbreads that were packed in 17 boxes = 105

Boxes of 7	Shortbreads	Boxes of 5	Shortbreads	Total shortbreads
17	119	0	0	119
16	112	1	5	117

If all the shortbreads are packed in boxes of 7, the number of shortbreads needed
= 17 x 7
= 119

Small difference
= 119 - 117
= 2

Big difference
= 119 - 105
= 14

Number of boxes of 5 shortbreads 
= 14 ÷ 2
= 7

Number of boxes of 7 shortbreads
= 17 - 7
= 10

Answer(s): (a) 105; (b) 10