Using a system of equations, it is found that she earns $5.5 for each hat and $7 for each scarf sold.
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
- Variable x: Cost of a hat.
- Variable y: Cost of a scarf.
One week she earns $114.00 by selling eight hats and 10 scarves, hence:
8x + 10y = 114.
The following week she sold 12 hats and six scarves and earned $108.00, hence:
12x + 6y = 108
Simplifying by 6:
2x + y = 18
y = 18 - 2x.
Replacing in the first equation:
8x + 10y = 114.
8x + 10(18 - 2x) = 114
12x = 66
x = 66/12
x = 5.5
y = 18 - 2x = 18 - 2 x 5.5 = 7.
More can be learned about a system of equations at brainly.com/question/24342899
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