Question

Kaelyn has some yarn that she 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. Kaelyn wants to make 3 times as many scarves as hats and use 5 kilograms of yarn. Let h be the number of hats Kaelyn makes and s be the number of scarves she makes.

Answer 1

s=3h

0.2h+0.1s=15

Explanation:

Answer 2

10 hats and 30 scarves

Explanation:

Let h be the number of hats Kaelyn makes and s be the number of scarves she makes.

Kaelyn wants to make 3 times as many scarves as hats, so

s = 3h

Each hat uses 0.2 kilograms of yarn, then h hats use 0.2h kg of yarn.

Each scarf uses 0.1 kilograms of yarn, then s scarves use 0.1s kg of yarn.

Kaelyn wants to use 5 kilograms of yarn, thus

0.2h + 0.1s = 5

You get the system of two equations:

`\left\{\begin{array}{l}s=3h\\ \\0.2h+0.1s=5\end{array}\right.`

Substitute the first equation into the second

`0.2h+0.1\cdot 3h=5\\ \\0.2h+0.3h=5\\ \\0.5h=5\\ \\5h=50\\ \\h=10\\ \\s=3\cdot 10=30`