555 grams of wool were needed to knit a sweater, a hat and a scarf. the hat required 5 times less wool than the sweater and 5 grams more than the scarf. how many grams of wool did each item require?

Let x grams used for sweater.

Then since hat required 5 times less wool than sweater

wool used for hat = x/6 (since 5 times less)

Scarf wool=wool for hat - 5

= x/6 -5

Total wool used = wool for sweater + hat + scarf

= x+x/6+x/6-5

Given total wool used = 555 gms.

i.e. x+x/6+x/6-5 = 555

8x/6= 560

x = 560(6/8) = 420

i.e. For sweater = 420 gm of wool

for hat = 70 gm of wool

and for scarf = 65 gm of wool were used.