The trick to solving this problem is to realize that the independent variable is x, which represents the number of people who can attend the party without the total party cost exceeding $80.
This is the form of the inequality:
(total cost) [less than or equal to] $80
(rent) + (cost per guest)(number of guests) [less than or equal to] $80
$45 + $5.50 x [less than or equal to] $80
Simplify. To do this, subtract $45 from both sides of this inequality.
Divide both sides of the resulting inequality by $5.50.
What is the restriction on x?
You can use a system of equations.
x=group 1
y=group 2
x+y=28
2x+4=y
Isolate the variable in equation 1.
y=-x+28
Substitute it into equation 2.
-x+28=2x+4
Solve.
-3x=-24
x=8
Substitute it into one of the equations for y.
-x+28=y
-8+28=y
y=20
There are 8 students in one group and 20 students in the other.
Hope this helps!
We can use a system of equations in order to solve for both of the numbers. Let's start off by assigning variables to each number. The bigger number can be 'x', and the smaller number can be 'y'.
We can make two equations from the given:
x = 18 + y
("One number is 18 more than another number")
x + y = 36
("The sum of the numbers is 36")
If you look at the first equation, the variable 'x' already has a value (18 + y). We can input its value into the second equation in order to solve for y:
x + y = 36
(18 + y) + y = 36
18 + 2y = 36
2y = 18
y = 9
Input the value of 'y' into the first equation:
x = 18 + y
x = 18 + 9
x = 27
<u>One number is 27 and the other number number is 9.</u>
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Let me know if you'd like me to explain anything I did here.
- breezyツ
