Question

Kate used 555 grams of wool to knit a sweater, hat, and scarf. She used 5 times less grams for the hat than for the sweater. She used 5 more grams for the hat than for the scarf. How many grams of wool did she use to knit for each?

(Give explanation)

Answer 1

Sweater: 392
`(6)/(7)`

Hat: 78
`(4)/(7)`

Scarf: 83
`(4)/(7)`

Explanation:

Set the sweater = x

The hat =
`(1)/(5)` x

The scarf =
`(1)/(5)` x + 5

x +
`(1)/(5)` x +
`(1)/(5)` x + 5 = 555

Combine like terms

1
`(2)/(5)` x + 5 = 555

Subtract 5 from both sides

1
`(2)/(5)` x = 550

Divide by 1
`(2)/(5)`

x = 392
`(6)/(7)` This is how much wool was used for the sweater.

Divide by 5 to get the hat = 78
`(4)/(7)`

Add 5 to that to get the scarf: 83
`(4)/(7)`