Answer:
10 hats and 30 scarves
Step-by-step 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:
[tex]\left\{\begin{array}{l}s=3h\\ \\0.2h+0.1s=5\end{array}\right.[/tex]
Substitute the first equation into the second
[tex]0.2h+0.1\cdot 3h=5\\ \\0.2h+0.3h=5\\ \\0.5h=5\\ \\5h=50\\ \\h=10\\ \\s=3\cdot 10=30[/tex]
