Question

Chevy has 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 use 2 kilograms of yarn to make a total of 15 items.
Let h be the number of hats Chevy makes and s be the number of scarves he makes.
Which system of equations represents this situation?​

Answer 1

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

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=(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`