Let us formulate the independent equation that represents the problem. We let x be the cost for adult tickets and y be the cost for children tickets. All of the sales should equal to $20. Since each adult costs $4 and each child costs $2, the equation should be
4x + 2y = 20
There are two unknown but only one independent equation. We cannot solve an exact solution for this. One way to solve this is to state all the possibilities. Let's start by assigning values of x. The least value of x possible is 0. This is when no adults but only children bought the tickets.
When x=0,
4(0) + 2y = 20
y = 10
When x=1,
4(1) + 2y = 20
y = 8
When x=2,
4(2) + 2y = 20
y = 6
When x=3,
4(3) + 2y= 20
y = 4
When x = 4,
4(4) + 2y = 20
y = 2
When x = 5,
4(5) + 2y = 20
y = 0
When x = 6,
4(6) + 2y = 20
y = -2
A negative value for y is impossible. Therefore, the list of possible combination ends at x =5. To summarize, the combinations of adults and children tickets sold is tabulated below:
Number of adult tickets Number of children tickets
0 10
1 8
2 6
3 4
4 2
5 0
The ratio of 7200 to 6400 equals 1.125 in decimal form. I hope this helps!:)
We have that
If you draw a diagram, and draw perpendiculars from the intersection to the sides of the rectangle, you will see they are the mid point of each side.
see the attached figure
<span>If the mid point of the smaller side is ---------> x.
The mid point of the larger side will be -----------> (x + 4) </span>
The full length if the smaller side will be 2x and the length of the larger side will be 2(x + 4) = 2x + 8
The perimeter = 2 times the length + 2 times the width.
2(2x + 8) + 4x = 56
4x + 16 + 4x = 56
8x = 40
x = 5
Therefore
length = 2x + 8 = 18cm
<span>width = 2x = 10cm
</span>
the answer is
<span>the lengths of the sides of the rectangle are
</span>
length = 18cm width = 10cm