How many of each type of table are there?

Question

At a wedding, there are tables that sit 4 people and tables that sit 6 people. If a total of 158 guests are at the

wedding and there are 33 tables, totally filled.

Answer 1

Hi Albee,

This is a substitution problem.

Let x be the table that fits 4 people and y be the table that fit 6 people.

There are 33 tables totally filled and this could includes both table that fits 4, which is x and table that fit 6, which is y.

Therefore, the equation we can come up with is x+y=33

Next, we know that there is a total of 158 guests that fit in all those 4-capacity tables and 6-capacity tables.

Therefore, we can come up with the second question: 4x + 6y = 158, with x be the # of table that fits 4 people and y is the # of table that fits 6 people.

So the two equations are:

x + y = 33

4x + 6y = 158

Now that you have 2 equations, let "manipulate" one equation, substitute to the other equation to find x and y.

Let's use the first equation because it will make our life much easier later.

If x + y = 33, we can also know that y = 33 - x. So now with this new equation, it seems like we are looking for y with this new equation.

So the new equations are:

y = 33 - x

4x + 6y = 158

Knowing that y is the what you get when 33 - x, we can substitube the expression into the second equation:

4x + 6(33-x) = 158

Basically, we are replacing y with '33-x' because that what's y would be, if you take 33-x.

Then we continue to simplify the second equation:

4x + 6(33-x) = 158. We then multiply 6 by 33 and 6 by x, which get us our equation below.

4x + 198 - 6x = 158. We can combine 4x and -6x, which gives us -2x, which is the next equation below.

-2x + 198 = 158 OR 198 - 2x = 158. These two equations are the same thing. At this point, it should be easy enough for you to find x value.

So x = 20 after all the calculation. Then we will plug this x value back to our original equations and it does not matter which one you pick, although picking the one with less coefficients would save you time and trouble.

x + y = 33

4x + 6y = 158

I pick the first equation again:

x + y = 33. Plug 20 in for x value.

20 + y = 33

You should get 13 as the y value.

So the # of table thats fits 4 people, which is x is 20.

The # of table that fits 6 people, which is y, is 13.

One way to check your answers is to look at the number and reason. If you get a decimal for the answer, you know you messed up somewhere during the manipulation or calculation part; there cannot a portion of a table, it need to be a whole number.

Hope this helps!