Answer :
Rounding to the nearest hundredth, we find that Xenia earned approximately 282.60 in the first two weeks of June.
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b
Let's start by finding Xenia's hourly wage, which we can use to calculate her earnings. We know that in the first week, when she worked 15 hours, she earned a certain amount, and in the second week, when she worked 22 hours, she earned 47.60 more than in the first week.
Let's use the variable x to represent Xenia's hourly wage. Then, in the first week, she earned:
15x dollars
In the second week, she earned:
22x + 47.60 dollars
We can now calculate her total earnings for the two weeks by adding up her earnings from the first and second weeks:
15x + (22x + 47.60) = 37x + 47.60 dollars
We don't know Xenia's hourly wage, but we do know that it must be the same in both weeks. This means that the x term is the same in both expressions above.
We can now use the information given in the problem to set up an equation:
22x + 47.60 = 15x + 47.60 + 47.60
The left-hand side represents Xenia's earnings in the second week, and the right-hand side represents her earnings in the first and second weeks combined. We added an extra 47.60 to the right-hand side to account for the fact that she earned that much more in the second week than in the first.
Simplifying the equation, we get:
7x = 47.60
Dividing both sides by 7, we find:
x = 6.80
So Xenia's hourly wage is 6.80.
To find her total earnings for the first two weeks of June, we can substitute x = 6.80 into our expression for her combined earnings:
37x + 47.60 = 37(6.80) + 47.60 \approx 282.60
Rounding to the nearest hundredth, we find that Xenia earned approximately 282.60 in the first two weeks of June.
To learn more about linear equation from the given link:
https://brainly.com/question/11897796
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