Step-by-step explanation:
Let x be the entry fee.
Let y be the cost of each ticket in dollars.
Since Keith paid the entry fee and 10 tickets,
we have x + 10y = $30.
In similar figures, the ratio between corresponding sides are the same.
![\frac{25}{35}=\frac{35}{49}](https://tex.z-dn.net/?f=%5Cfrac%7B25%7D%7B35%7D%3D%5Cfrac%7B35%7D%7B49%7D)
Simplify the two to see that they are equal.
The top and bottom of the left fraction are divisible by 5.
The top and bottom of the right fraction are divisible by 7.
![\frac{5}7=\frac{5}7](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D7%3D%5Cfrac%7B5%7D7)
Of course, the dimensions of that third picture would have to be this fraction.
Let's test these answers.
![\frac{5}6\neq\frac{5}7](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D6%5Cneq%5Cfrac%7B5%7D7)
⇒ A is not a solution
![\frac{30}{42}=\frac{5}7](https://tex.z-dn.net/?f=%5Cfrac%7B30%7D%7B42%7D%3D%5Cfrac%7B5%7D7)
⇒
B is the solution
(divide the top and bottom by 6)
Y=mx+b
b= -2
m= rise/run = 2/3
y=2/3x-2
9514 1404 393
Answer:
x = 7 1/3
Step-by-step explanation:
The smaller triangle is 6/9 = 2/3 the size of the larger triangle, so the left side is ...
(x -2) = (2/3)(8)
3(x -2) = 16 . . . . . multiply by 3 to clear fractions
3x -6 = 16 . . . . . . eliminate parentheses
3x = 22 . . . . . . . . add 6; next divide by 3*
x = 22/3 = 7 1/3 . . . . . feet
_____
* Note that we multiplied by 3, then divided by 3. If you're comfortable working with fractions and/or mixed numbers, these steps are unnecessary. The answer is simply x = 2 + 16/3 = 22/3.