a) Amount spent on socks: $75
Number of items: Between 4 – 8 (3 socks and between 1 – 5 shoes)
Based on the fact that (Amount spent on shoes = Total amount spent – amount spent on socks)
We know that amount spent on shoes needs to be a whole number, and the amount spent on socks is already a whole number ($75). Therefore, the Total amount spent must also be a whole number (Whole number – whole number = whole number).
Total amount spent = Average cost of items x total number of items
The average cost of items is $78.60 so we need to find a number less than 8 that when multiplied by $78.60, will give a whole number as the product. The only possible number is 5, so Mr Chua bought 5 items in total. 5 items minus the three socks means he bought 2 pairs of shoes.
b) Total amount spent = $78.60 x 5
Amount spent on shoes = $393 – $75
Average price of each pair of shoes = $318 ÷ 2