Answer:
x = 35 Â Â y = 45
Step-by-step explanation:
Total number of strings:  x + y = 80  ⇒  x = 80 - y
Substitute  x = 80 - y  into  4.5x + 1.5y = 225  to find y:
4.5(80 - y) + 1.5y = 225
360 - 4.5y + 1.5y = 225
           3y = 135
            y = 45
Substitute the found value of y into  x + y = 80  to find x:
x + 45 = 80
x = 80 - 45 = 35
To solve the problem we must know about the system of equations.
A system of equations to have no real solution, the lines of the equations must be parallel to each other.
1. Dependent Consistent System
A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.
The number of premium and standard strings Kenny ordered are 35 and 45 respectively.
Given to us
Total Number of Strings
= number of premium strings + number of standard strings
80 = x+ y
Solving for y,
y = 80-x
Total Cost of all strings
($4.50)x + ($1.50y) = $225
4.50x + 1.50y = 225
Substitute the value of y,
[tex]4.50x + 1.50(80-x) = 225\\\\4.50x +120 -1.5x = 225\\\\4.50x-1.5x = 225-120\\\\3x = 105\\\\x=\dfrac{105}{3}\\\\x = 35[/tex]
Thus, the number of premium strings Kenny ordered was 35.
Substitute the value of x in the equation of y,
y = 80 - x
y = 80 - 35
y = 45
Thus, the number of standard strings Kenny ordered was 45.
Hence, the number of premium and standard strings Kenny ordered are 35 and 45 respectively.
Learn more about System of Equations:
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