Question 895979: I need help converting a word problem into an algebraic equation
here is the problem
1 table seats 5 people
2 tables seat 8 people
3 tables seat 11 people
how many people will 12 tables seat?
Marsha thinks that if she has to set up the conference room with tables to seat 39 people she will need 12 tables. show why she is wrong
create a model for this situation
Found 3 solutions by jim_thompson5910, richwmiller, Theo:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Each time you're adding 3 (5 to 8, 8 to 11)
So the rate of change is 3 people per table, which represents the slope.
So m = 3/1 = 3
Let x = number of tables, y = number of people
"1 table seats 5 people" means x = 1, y = 5
y = mx+b
y = 3x+b
5 = 3*1+b
5 = 3+b
5-3 = b
2 = b
b = 2
So the model is y = 3x+2
Notice how if we have 3 tables for instance, then x = 3
y = 3x+2
y = 3*3+2
y = 11
which reflects the fact "3 tables seat 11 people"
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If we have 39 people, then y = 39. Let's find x
y = 3x+2
39 = 3x+2
39-2 = 3x
37 = 3x
3x = 37
x = 37/3
x = 12.3333...
Round that up to go from 12.3333.... to 13
You'll need 13 tables. Twelve of those tables will have 3*12+2 = 38 people and that last table (the thirteenth table) will have 39-38 = 1 person.
Of course, you can move people around and have the structure of some tables different, but overall you need 13 tables.
If she had just 12 tables, then one person would be left out.
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website!
An = A1 + (n - 1)*d
1 table seats 5 people
2 tables seat 8 people
3 tables seat 11 people
4 14
5 17
6 20
7 23
8 26
9 29
10 32
11 35
12 38 12 tables seat 38
13 41
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! marsha thinks she needs 12 tables to seat 39 people.
1 table seats 5
2 tables seat 8
3 tables seat 11
the first table seats 5.
each additional table seats 3 additional people.
12 tables in total is equal to the first table plus 11.
the number of people that can be seated is equal to 5 at the first table and 3 at each of the 11 additional tables.
the total number of people that can be seated is therefore 5 + 3 * 11 = 5 + 33 which is equal to 38.
she needs to seat 39 people so 12 tables is not enough.
she needs 13 tables in total.
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