Catholic High Sch 2006 PSLE Math Prelim Q46

Mary and Jane bought some utensils consisting of forks and spoons from a departmental store. Jane bought 2/5 of the total utensils. Altogether, they bought 30 more spoons than forks. Mary bought 2/3 of the spoons and ½ of the forks. How many utensils did Jane buy?

Solution

All utensils ----
Spoons ----- 6 units + 30
Forks ----- 6 units
(6 units is used because 6 it can be split up into thirds and halves – 2/3 spoons, ½ forks)

Mary bought -----
Spoons ----- 4 units + 20 (working; 2/3 x 6u + 2/3 x 30 spoons)
Forks ----- 3 units (working; 1/2 of 6u is 3u)
Altogether for Mary ----- 7 units + 20 (which is 3/5 of utensils)

Jane bought the remaining utensils which is -----
Spoons ----- 6 units + 30 – 4 units – 20 = 2 units + 10
Forks ----- 6 units – 3 units = 3 units
Altogether for Jane ----- 5 units + 10 (which is 2/5 of the utensils)

(Mary) 7 units + 20 ----- 3/5 (x5)
(Jane) 5 units + 10 ----- 2/5 (x7)

(Mary) 35 units + 100 ----- 15/5
(Jane) 35 units + 70 ----- 14/5

(Mary) – (Jane)
35 units + 100 – 35 units – 70 ----- 15/5 – 14/5
30 ----- 1/5 (of utensils)
2/5 of utensils ----- 2 x 30 = 60

Answer: Jane bought 60 utensils.