your friend rents 10 chairs and 2 tables for $300. Another friend rents 8 chairs and 4 tables for $300. How much do you expect to pay for each table and chair?

Question

What would the Equation 1 and Equation 2 be?

Answer 1

Hi Storm,

 

Let's say c represents the number of chairs and t represents the number of tables.

 

That would mean that your friend rents 10c + 2t for $300, or 10c + 2t = 300.

 

Your other friend rents 8c + 4t for $300, or 8c + 4t = 300.

 

To calculate the price for each item, we can and shall use substitution. But let's first simplify them. We can divide the first equation by 2 and the second by 4, since these are the smallest numbers in their respective equations.

 

That gives us 5c + t = 150 and 2c + t = 75.

 

Now we substitute!

 

Using the second equation: t = 75 - 2c (subtract 2c from both sides)

 

5c + (75 - 2c) = 150

 

3c = 75

 

c = 25, or $25

 

Plugging into any equation given (I will use the second equation since it looks simpler.):

 

t = 75 - 2 * 25

 

t = 75 - 50

 

t = 25, or $25

 

Hope this helps!