Answer: [tex]\left \{ {{0.2h+0.1s=2} \atop {h+s=15}} \right.[/tex]
Step-by-step explanation:
According to the exercise, we know that:
[tex]h[/tex]: Number of hats Chevy makes.
[tex]s[/tex]: number of scarves Chevy makes,
He wants to use 2 kilograms of yarn.
Knowing that each hat uses 0.2 kilograms of yarn and each scarf uses 0.1 kilograms of yarn, we can write the following equation to represent this situation:
[tex]0.2h+0.1s=2[/tex]
Since Chevy wants to make 15 items in total, we can write this equation:
[tex]h+s=15[/tex]
Finally, having these equations, we can set up the following system of equations that represents this situation:
[tex]\left \{ {{0.2h+0.1s=2} \atop {h+s=15}} \right.[/tex]
To solve it we can use the Substitutition Method. The steps are:
1. Solve for "s" from the second equation:
[tex]s=15-h[/tex]
2. Substitute the equation above into the first equation and solve for "h":
[tex]0.2h+0.1(15-h)=2\\\\0.2h+1.5-0.1h=2\\\\0.1h=2-1.5\\\\h=\frac{0.5}{0.1}\\\\h=5[/tex]
3. Substitute the value of "h" into [tex]s=15-h[/tex] to find the value of "s". Then:
[tex]s=15-5\\\\s=10[/tex]
