Kayla is working two summer jobs, making $10 per hour lifeguarding and $21 per hour tutoring. Last week Kayla worked 4 times as many hours tutoring as she worked lifeguarding and earned a total of $188. Write a system of equations that could be used to determine the number of hours Kayla worked lifeguarding last week and the number of hours she worked tutoring last week. Define the variables that you use to write the system.
Give 2 systems of equations
Let's define the variables:
Let x represent the number of hours Kayla worked lifeguarding last week.
Let y represent the number of hours Kayla worked tutoring last week.
First system of equations:
From the problem, we know that Kayla makes $10 per hour lifeguarding and $21 per hour tutoring. The total amount of money she made is $188. Therefore, we can write the first equation as:
10x + 21y = 188
Additionally, the problem states that she worked 4 times as many hours tutoring as she worked lifeguarding. Mathematically, we can express this relationship as:
y = 4x
Writing both equations together, we have the first system of equations:
10x + 21y = 188
y = 4x
Second system of equations:
Alternatively, we can rewrite the second equation as:
x = y/4
Substituting this into the first equation, we have:
10(y/4) + 21y = 188
2.5y + 21y = 188
23.5y = 188
y = 8
Substituting this value of y into the second equation, we have:
x = 8/4
x = 2
Therefore, the second system of equations is:
x = 2
y = 8
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Let's define the variables to write the system of equations:
Let's assume the number of hours Kayla worked lifeguarding is 'x'.
Let's assume the number of hours Kayla worked tutoring is 'y'.
System of Equations 1:
From the given information, we know that Kayla made $10 per hour lifeguarding and $21 per hour tutoring.
So, the equation representing the total amount earned can be defined as:
10x + 21y = 188 ---(Equation 1)
Additionally, we are told that Kayla worked 4 times as many hours tutoring as she worked lifeguarding. So, the second equation representing this can be written as:
y = 4x ---(Equation 2)
System of Equations 2:
In this system, we can rearrange Equation 2 to represent 'x' in terms of 'y' and substitute it into Equation 1.
Since y = 4x, we can rewrite this equation as x = (1/4)y.
Substituting this expression for 'x' in Equation 1, we get:
10(1/4)y + 21y = 188
(10/4)y + 21y = 188
(5/2)y + 21y = 188
(5y/2) + 21y = 188
(5y + 42y)/2 = 188
47y/2 = 188
47y = 376
y = 376/47
y = 8
Now, substituting this value of 'y' back into Equation 2, we can find the value of 'x':
x = (1/4)(8)
x = 2
Therefore, the solution of System of Equations 2 is x = 2 and y = 8.