Question 1205255: WHAT IF? You decide to rent tables from a different company. The situation can be modeled by the equation 4x+6y=180, where x is the number of small tables and y is the number of large tables.
a. Interpret the terms and coefficients in the equation.
I thought it meant what the solution was but I don't know what it means by that so can you help me please? Thank you so much!
Found 4 solutions by ikleyn, greenestamps, Edwin McCravy, math_tutor2020:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
WHAT IF? You decide to rent tables from a different company. The situation can be modeled by the equation 4x+6y=180,
where x is the number of small tables and y is the number of large tables.
a. Interpret the terms and coefficients in the equation.
I thought it meant what the solution was but I don't know what it means by that so can you help me please? Thank you so much!
~~~~~~~~~~~~~~~~~~~~~~
The last line of your post (before the words " Thank you so much ! ") is meaningless.
The problem's formulation goes not far from it, too.
In order for the problem would make sense, it should be totally re-written.
Saying " totally ", I mean - - - from scratch and at other level.
Treating nonsense in any form is not a profile of this forum.
Have a nice day ( ! )
Consider to hire 3 - 5 - 7 mathematically literate specialists
to write, re-write, edit, re-edit your writing after you.
Or to compose math problems instead of you and/or instead of your professor . . . ,
because in such form it should not go out . . .
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
It is certainly true that both the presentation of the problem and the question you ask need a lot of improvement....
However, it is clear what the intent of the problem is, so I will move on with it.
The problem is about renting tables, so the equation is obviously a cost equation, showing that the cost of the small tables plus the cost of the large tables is the total cost.
The equation is 4x+6y=180; and we are told that x is the number of small tables and y is the number of large tables. That clearly means that 4x is the total cost of the small tables, which means the cost to rent each small table is $4; and similarly $6 is the cost to rent each large table.
Now to the question that is asked: "Interpret the terms and coefficients in the equation."
The terms in an equation are the things that are added together, or that stand by themselves. The terms in this equation are 4x, 6y, and 180. Those terms are, as described above, the cost of the small tables, the cost of the large tables, and the total cost.
The coefficients in an equation are the numerical parts of the terms that contain variables. 4x is a term; the coefficient there is "4"; 6y is a term; the coefficient there is "6". As described earlier, the interpretation of those coefficients is that they are the cost for renting each small table and each large table.
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website!
Small tables rent for $4 each. Large tables rent for $6 each.
You want to rent somewhere between 30 and 45 tables. But you
only want to spend $180.
The 4 says the cost to rent 1 small table is $4.
The 6 says the cost to rent 1 large table is $6.
The 180 says you have $180 to spend to rent tables.
You have 16 possibilities:
1. 0 small tables at $4 each for $0 and 30 large tables for $6 each for
$180. Total $180
2. 3 small tables at $4 each for $12 and 28 large tables for $6 each for
$168. Total $180
3. 6 small tables at $4 each for $24 and 26 large tables for $6 each for
$156. Total $180
4. 9 small tables at $4 each for $36 and 24 large tables for $6 each for
$144. Total $180
5. 12 small tables at $4 each for $48 and 22 large tables for $6 each for
$132. Total $180
6. 15 small tables at $4 each for $60 and 20 large tables for $6 each for
$120. Total $180
7. 18 small tables at $4 each for $72 and 18 large tables for $6 each for
$108. Total $180
8. 21 small tables at $4 each for $84 and 16 large tables for $6 each for
$96. Total $180
9. 24 small tables at $4 each for $96 and 14 large tables for $6 each for
$84. Total $180
10. 27 small tables at $4 each for $108 and 12 large tables for $6 each for
$72. Total $180
11. 30 small tables at $4 each for $120 and 10 large tables for $6 each for
$60. Total $180
12. 33 small tables at $4 each for $132 and 8 large tables for $6 each for
$48. Total $180
13. 36 small tables at $4 each for $144 and 6 large tables for $6 each for
$36. Total $180
14. 39 small tables at $4 each for $156 and 4 large tables for $6 each for
$24. Total $180
15. 42 small tables at $4 each for $168 and 2 large tables for $6 each for
$12. Total $180
16. 45 small tables at $4 each for $180 and 0 large tables for $6 each for
$0. Total $180
You can take your pick of these 16 choices for spending your $180 to rent tables.
Edwin
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
x = number of small tables
4x = cost of just those small tables only
The coefficient 4 means "it costs $4 per small table".
y = number of large tables
6y = cost of just those large tables only
The coefficient 6 means "it costs $6 per large table".
4x+6y = total cost
4x+6y = 180 means you want the total cost to be $180
One solution, of many, is x = 0 and y = 30
x = 0 small tables costs 4x = 4*0 = 0 dollars
y = 30 large tables costs 6y = 6*30 = 180 dollars
total cost = 0+180 = 180
Another solution would be x = 3 and y = 28.
Each time x goes up by 3, y drops by 2. This is from the slope -2/3. Note that solving 4x+6y = 180 leads to y = (-2/3)x+30.
If x = 3 small tables and y = 28 large tables are rented, then you spend a total of 4*x+6*y = 4*3+6*28 = 12+168 = 180 dollars.
Here is a list of all possible nonnegative integer solutions
(0, 30), (3, 28), (6, 26), (9, 24), (12, 22), (15, 20),
(18, 18), (21, 16), (24, 14), (27, 12), (30, 10), (33, 8),
(36, 6), (39, 4), (42, 2), (45, 0)
There are 16 solutions in that list. Each solution is of the form (x,y).
The list was generated using the sequence command in GeoGebra.
All of the points mentioned are on the line 4x+6y = 180 aka 2x+3y = 90 aka y = (-2/3)x+30.
Desmos or GeoGebra or similar can be used to graph.
|
|
|
