it says the knights banquet hall uses the equation 25n-c+1250=0 determine the cost for a hall rental
the legions banguet hall usues the equation 30n+995-c=0 to determine the cost for thier hall rental
express each equation in slope y-intercept form- c=mn+b
identify the fixeed and variable costs for each hall
What is the cost at each hall for a graduation banquet for 45 people
Which hall offers the better price comment on wether your conclusion changes if a few more people wish to attend
oh and this is grade nine math
To express each equation in slope-intercept form (c=mn+b), we need to rearrange the given equations.
1. Knights Banquet Hall equation: 25n - c + 1250 = 0
To express it in slope-intercept form, we isolate c:
- c = -25n + 1250
- c = (-25)n + 1250
The slope (m) in this case is -25, and the y-intercept (b) is 1250.
2. Legions Banquet Hall equation: 30n + 995 - c = 0
Rearranging to slope-intercept form:
- c = -30n - 995
- c = (-30)n - 995
The slope (m) here is -30, and the y-intercept (b) is -995.
The fixed cost represents the constant term in the equation, which is the y-intercept (b). The variable cost depends on the number of people (n) and is represented by the coefficient of n.
Now, let's determine the cost at each hall for a graduation banquet with 45 people:
1. Knights Banquet Hall:
- Using the equation - c = -25n + 1250, plug in n = 45:
- c = -25(45) + 1250
- c = -1125 + 1250
- c = 125
Therefore, the cost to rent the Knights Banquet Hall for 45 people is $125.
2. Legions Banquet Hall:
- Using the equation - c = -30n - 995, substitute n = 45:
- c = -30(45) - 995
- c = -1350 - 995
- c = -2345
So, the cost to rent the Legions Banquet Hall for 45 people is $2,345.
Based on these calculations, it appears that the Knights Banquet Hall offers a better price for a graduation banquet with 45 people, as it only costs $125 compared to the Legions Banquet Hall's cost of $2,345.
If a few more people wish to attend, you can simply substitute the new number of attendees into the equations and recalculate the costs at each hall. The conclusion may or may not change depending on the specific values of the additional attendees and the coefficients in the equations.