Respuesta :
Answer:
She bought 8 large frames and 18 small frames of each type.
Step-by-step explanation:
Given:
A woman bought some large frames for $11 each and some small frames for $8 each at a closeout sale.
If she bought 26 frames for $232.
Now, to find each type she bought.
Let the number of large frames for $11 be [tex]x.[/tex]
And let the number of small frames for $8 be [tex]y.[/tex]
So, the total number of frames:
[tex]x+y=26[/tex]
[tex]x=26-y\ \ \ \ .........(1)[/tex]
Now, the total cost of frames:
[tex]11x+8y=232[/tex]
Substituting the value of [tex]x[/tex] from equation (1) we get:
[tex]11(26-y)+8y=232[/tex]
[tex]286-11y+8y=232[/tex]
[tex]286-3y=232[/tex]
Subtracting both by sides 286 we get:
[tex]-3y=-54[/tex]
Dividing both sides by -3 we get:
[tex]y=18.[/tex]
The number of small frames = 18.
Now, substituting the value of [tex]y[/tex] in equation (1) to get the value of [tex]x[/tex]:
[tex]x=26-y\\\\x=26-18\\\\x=8.[/tex]
The number of large frames = 8.
Therefore, she bought 8 large frames and 18 small frames of each type.
