The cost of 7 chairs and 2 tables is equal.If the cost of 6 chairs and 5 tables is 10575, find the cost of 12 chairs.​

Sagot :

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.