Question

Chevy has some yarn that he wants to use to make hats and scarves. Each hat uses 0.2 kilograms of yarn and

Answer 1

Answer: $\left \{ {{0.2h+0.1s=2} \atop {h+s=15}} \right.$

Step-by-step explanation:

According to the exercise, we know that:

$h$: Number of hats Chevy makes.

$s$: 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:

$0.2h+0.1s=2$

Since Chevy wants to make 15 items in total, we can write this equation:

$h+s=15$

Finally, having these equations, we can set  up the following system of  equations that represents this situation:

$\left \{ {{0.2h+0.1s=2} \atop {h+s=15}} \right.$

To solve it we can use the Substitutition Method. The steps are:

1. Solve for "s" from the second equation:

$s=15-h$

2. Substitute the equation above into the first equation and solve for "h":

$0.2h+0.1(15-h)=2\\\\0.2h+1.5-0.1h=2\\\\0.1h=2-1.5\\\\h=\frac{0.5}{0.1}\\\\h=5$

3. Substitute the value of "h" into $s=15-h$ to find the value of "s". Then:

$s=15-5\\\\s=10$