Respuesta :
Answer:
Number of fancy shirts Kris bought = 2
Number of plain shirts Kris bought = 5
Step-by-step explanation:
Total number of shirts = 7
Let number of fancy shirts be = [tex]x[/tex]
Let number of plain shirts be = [tex]y[/tex]
Total number of shirts = [tex]x+y[/tex]
So, we have a sum equation as:
[tex]x+y=7[/tex]
Total cost of shirts = $131
Cost of a fancy shirt = $28
Cost of [tex]x[/tex] fancy shirts in dollars can be given as = [tex]28x[/tex]
Cost of a plain shirt = $15
Cost of [tex]y[/tex] plain shirts in dollars can be given as = [tex]15y[/tex]
Total cost of shirts = [tex]28x+15y[/tex]
So, we have a cost equation as:
[tex]28x+15y=131[/tex]
The system of equations is :
A) [tex]x+y=7[/tex]
B) [tex]28x+15y=131[/tex]
Rearranging equation A, to solve for [tex]y[/tex] in terms of [tex]x[/tex]
Subtracting both sides by [tex]x[/tex]
[tex]x+y-x=7-x[/tex]
[tex]y=7-x[/tex]
Substituting value of [tex]y[/tex] we got from A into equation B.
[tex]28x+15(7-x)=131[/tex]
Using distribution.
[tex]28x+105-15x=131[/tex]
Simplifying.
[tex]13x+105=131[/tex]
Subtracting both sides by 105.
[tex]13x+105-105=131-105[/tex]
[tex]13x=26[/tex]
Dividing both sides by 13.
[tex]\frac{13x}{13}=\frac{26}{13}[/tex]
[tex]x=2[/tex]
We can plugin [tex]x=2[/tex] in the rearranged equation A to get value of [tex]y[/tex]
[tex]y=7-2[/tex]
∴[tex]y=5[/tex]
So, number of fancy shirts Kris bought = 2
Number of plain shirts bough = 5
