Question

chevy have some yarn that he wants to use to make hats and scarves. each hat uses 0.2 kilograms of yarn and each scarf uses 0.1 kilograms of yarn. chevy wants to make a total of 15 items. let h be the number of hats chevy makes and s be number of scarves he makes.

Answer 1

`The\ following\ system\ of\ equations\ gives\ number\ of\ hats\ and\ scarves\\\\h+s=15\\\\0.2h+0.1s=k\\\\Where\ k\ is\ total\ yarn\ in\ kg.\\\\If\ k=2\ kg\\\\h=5\ hats,\ s=10\ scarves`

Explanation:

`Number\ of\ hats=h\\\\Number\ of\ scarves=s`

Total Number of items:

`Total\ items=15\\\\Total\ number\ of\ items=Number\ of\ hats+Number\ of\ scarves\\\\Total\ Number\ of\ items=h+s\\\\h+s=15.......................................eq(1)`

Total yarn used:

`Yarn\ used\ in\ 1\ hat=0.2\ kg\\\\Yarn\ used\ in 1\ scarf=0.1\ kg\\\\Yarn\ used\ in\ hats=Yarn\ used\ in\ 1\ hat* Number\ of\ hats\\\\Yarn\ used\ in\ hats=0.2* h=0.2h\\\\Yarn\ used\ in\ scarves=Yarn\ used\ in\ 1\ scarf* Number\ of\ scarves\\\\Yarn\ used\ in\ hats=0.1* s=0.1s\\\\Total\ yarn\ used=0.2h+0.1s\\\\If\ total\ yarn=k\ kg\\\\Solution\ of\ following\ system\ of\ equations\ gives\ number\ of\ hats\ and\ scarves\\\\h+s=15\\\\0.2h+0.1s=k`

`if\ k=2\\\\h+s=15...............eq(2)\\\\0.2h+0.1s=2.......eq(3)\\\\eq(2)-0.2* eq(3)\\\\0.1s=1\\\\s=10\\\\From\ eq(2)\\\\h=15-s\\\\h=5\ hats`