The library in Geotown has a large room with enough tables and chairs to seat 236 people. Some of the tables are in shape of hexagon and seat six people each. The rest of the tables are octagonal and seat eight people each. If there are 35 tables in the room, how many are hexagons and how many are octagons?

Question

The library in Geotown has a large room with enough tables and chairs to seat 236 people.  Some of the tables are in shape of hexagon and seat six people each.  The rest of the tables are octagonal and seat eight people each.  If there are 35 tables in the room, how many are hexagons and how many are octagons?

vertcoolname · Answer

easy algebra equation
2 variables

OLIVER69 · Answer

h + o = 35
then
6h + 8c = 236

h = 22
y = 13
(I hoped I could help)

mikewwe13 · Answer

Let x be the number of hexagonal tables and y be the number of octagonal tables. Then we can set up a system of two equations to represent the given information:

x + y = 35    (the total number of tables is 35)
6x + 8y = 236  (the total number of seats is 236)

To solve for x and y, we can use substitution or elimination. Here, we'll use elimination.

Multiply the first equation by 6 to get:

6x + 6y = 210

Subtract this equation from the second equation to eliminate x:

6x + 8y = 236
- (6x + 6y = 210)
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2y = 26

So y = 13, which means there are 13 octagonal tables. Substituting this into the first equation, we get:

x + 13 = 35

So x = 22, which means there are 22 hexagonal tables.

Therefore, there are 22 hexagonal tables and 13 octagonal tables in the room.