Answer:
Option C) 27 people
Step-by-step explanation:
Let
x ----> the number of people
we know that
The cost of decorations ($35) plus the number of people (x) multiplied by the cost per person on food ($8.50) must be equal to $264.50
so
The linear equation that represent this situation is

solve for x
Subtract 35 both sides


Divide by 8.50 both sides


The third option should be correct
Answer:
P = 9 is the max value
Step-by-step explanation:
Sketch
2x + 4y = 10
with x- intercept = (5, 0) and y- intercept (0, 2.5)
x + 9y = 12
with x- intercept = (12, 0) and y- intercept = (0,
)
Solve
2x + 4y = 10 and x + 9y = 12 to find the point of intersection at (3, 1)
The region corresponding to the solution of the system of constraints
Has vertices at (0,
), (0, 0) , (5, 0) and (3, 1)
Now evaluate the objective function at each vertex.
(0, 0) can be excluded as it will not give a maximum
(5, 0) → P = 5 + 0 = 5
(0,
) → 0 + 8 = 8
(3, 1) → 3 + 6(1) = 3 + 6 = 9 ← maximum value
Thus the maximum value is 9 when x = 3 and y = 1
Answer:
x = 0.667 and y = -0.6
Step-by-step explanation:
Given that,
6x + 5y = 1 ....(1)
6x - 5y = 7 ...(2)
We need to solve the above equations.
Subtract equations (1) and (2)
6x + 5y -(6x - 5y) = 1-7
6x+5y-6x+5y = -6
10y=-6
y = -0.6
Put the value of y in equation (1).
6x + 5(-0.6) = 1
6x = 1-5(-0.6)
6x = 4
x = 0.667
Hence, first step is to subtract equation (1) and (2) then put the value of y in equation (1).
You have to divide both 9 & 6 by their greatest common factor which is 3 so the answer is 3
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