Answer:
5400
Step-by-step explanation:
Let x represent the cost of a chair and y represent the cost of a table. We can use this to set up a system of equations:
7x=2y
6x+5y=10575
We can solve this system using substitution.
Start by rewriting the first equation in terms of x.
[tex]7x=2y\\\text{Divide both sides by 7}\\x=\frac{2}{7}y[/tex]
Substitute this into the second equation:
[tex]6(\frac{2}{7}y)+5y=10575\\\frac{12}{7}y+5y+10575\\\frac{12}{7}y+\frac{35}{7}y=10575\\\frac{47}{7}y=10575[/tex]
Multiply both sides by 7
[tex]47y=74025[/tex]
Divide both sides by 47
[tex]y=1575[/tex]
This means...
[tex]7x=2(1575)\\7x=3150[/tex]
Divide both sides by 7
[tex]x=450[/tex]
One chair costs 450. Now, multiply this number by 12 to find the cost of 12 chairs.
[tex]450*12=5400[/tex]
12 chairs cost 5400.
