**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.**

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