Answer: Fraction of twins =
Fractions of triplets =
Fractions of quadruplets = 
Step-by-step explanation:
Since we have given that
Number of set of twins = 5
Number of sets of triplets = 2
Number of sets of quadruplets = 1
Total number of sets is given by

Now, we need to find the fraction of those students.
So, Fraction of twins is given by

Fractions of triplets is given by

Fractions of quadruplets is given by

<u>Part (a)</u>
The variable y is the dependent variable and the variable x is the independent variable.
<u>Part (b)</u>
The cost of one ticket is $0.75. Therefore, the cost of 18 tickets will be:
dollars
Now, we know that Kendall spent her money only on ride tickets and fair admission and that she spent a total of $33.50.
Therefore, the price of the fair admission is: $33.50-$13.50=$20
If we use y to represent the total cost and x to represent the number of ride tickets, the linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission can be written as:
......Equation 1
<u>Part (c)</u>
The above equation is logical because, in general, the total cost of the rides will depend upon the number of ride tickets bought and that will be 0.75x. Now, even if one does not take any rides, that is when x=0, they still will have to pay for the fair admission, and thus their total cost, y=$20.
Likewise, any "additional" cost will depend upon the number of ride tickets bought as already suggested. Thus, the total cost will be the sum of the total ride ticket cost and the fixed fair admission cost. Thus, the above Equation 1 is the correct representative linear equation of the question given.
x = total amount split between Adam and Tom.
since we know the total amount split between both in a 18 : 17 ratio is "x", let's divide "x" by (18 + 17) and distribute accordingly to get the amount of each.
![\stackrel{Adam~received}{18\cdot \cfrac{x}{18+17}}\qquad \qquad \stackrel{Tom~received}{17\cdot \cfrac{x}{18+17}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that Adam got "5" more}}{ \stackrel{Adam}{18\cdot \cfrac{x}{18+17}}~~ = ~~\stackrel{Tom}{17\cdot \cfrac{x}{18+17}~~ + ~~5} }\qquad \implies \qquad \cfrac{18x}{35}~~ + ~~\cfrac{17x}{35}+5](https://tex.z-dn.net/?f=%5Cstackrel%7BAdam~received%7D%7B18%5Ccdot%20%5Ccfrac%7Bx%7D%7B18%2B17%7D%7D%5Cqquad%20%5Cqquad%20%5Cstackrel%7BTom~received%7D%7B17%5Ccdot%20%5Ccfrac%7Bx%7D%7B18%2B17%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bsince%20we%20know%20that%20Adam%20got%20%225%22%20more%7D%7D%7B%20%5Cstackrel%7BAdam%7D%7B18%5Ccdot%20%5Ccfrac%7Bx%7D%7B18%2B17%7D%7D~~%20%3D%20~~%5Cstackrel%7BTom%7D%7B17%5Ccdot%20%5Ccfrac%7Bx%7D%7B18%2B17%7D~~%20%2B%20~~5%7D%20%7D%5Cqquad%20%5Cimplies%20%5Cqquad%20%5Ccfrac%7B18x%7D%7B35%7D~~%20%2B%20~~%5Ccfrac%7B17x%7D%7B35%7D%2B5)
![\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{18x}{35} \right)~~ = ~~35\left( \cfrac{17x}{35}+5 \right)}\implies 18x~~ = ~~17x+175\implies \boxed{x =175} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Tom~received}{17\cdot \cfrac{x}{18+17}}\implies \cfrac{17(175)}{35}\implies \blacktriangleright 85 \blacktriangleleft](https://tex.z-dn.net/?f=%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B35%7D%7D%7B35%5Cleft%28%20%5Ccfrac%7B18x%7D%7B35%7D%20%5Cright%29~~%20%3D%20~~35%5Cleft%28%20%5Ccfrac%7B17x%7D%7B35%7D%2B5%20%5Cright%29%7D%5Cimplies%2018x~~%20%3D%20~~17x%2B175%5Cimplies%20%5Cboxed%7Bx%20%3D175%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7BTom~received%7D%7B17%5Ccdot%20%5Ccfrac%7Bx%7D%7B18%2B17%7D%7D%5Cimplies%20%5Ccfrac%7B17%28175%29%7D%7B35%7D%5Cimplies%20%5Cblacktriangleright%2085%20%5Cblacktriangleleft)
22.5/(x-6) + 22.5/(x+6) = 9
multiply by x-6
=> (x-6)22.5/(x-6) + (x-6)22.5/(x+6) = 9(x-6)
=> 22.5 + (x-6)22.5/(x+6) = 9(x-6)
multiply by x+6
=> (x+6)22.5 + (x+6)(x-6)22.5/(x+6) = 9(x-6)(x+6)
=> (x+6)22.5 + (x-6)22.5 = 9(x-6)(x+6)
distribute
=> 22.5x+6(22.5) + 22.5x - 6(22.5) = 9(x^2 - 36)
=> 45x = 9x^2 - 9(36)
=> 0 = 9x^2 - 45x - 9(36)
divide by 9
=> 0 = x^2 - 5x - 36
=> 0 = x^2 - 5x - 36
=> 0 = (x - 9)(x + 4)
x=9 and -4